Physics-
General
Easy

Question

The figure shows a glass tube (linear co-efficient of expansion is alpha) completely filled with a liquid of volume expansion co-efficient gamma. On heating length of the liquid column does not change. Choose the correct relation between gamma and alpha

  1. gamma equals alpha    
  2. gamma equals 2 alpha    
  3. gamma equals 3 alpha    
  4. gamma equals fraction numerator alpha over denominator 3 end fraction    

The correct answer is: gamma equals 2 alpha


    When length of the liquid column remains constant, then the level of liquid moves down with respect to the container, thus gamma must be less than 3 alpha
    Now we can write V equals V subscript 0 end subscript left parenthesis 1 plus gamma increment T right parenthesis
    Since V equals A l subscript 0 end subscript equals open square brackets A subscript 0 end subscript open parentheses 1 plus 2 alpha increment T close parentheses close square brackets l subscript 0 end subscript equals V subscript 0 end subscript open parentheses 1 plus 2 alpha increment T close parentheses
    Hence V subscript 0 end subscript open parentheses 1 plus gamma increment T close parentheses equals V subscript 0 end subscript open parentheses 1 plus 2 alpha increment T close parentheses rightwards double arrow gamma equals 2 alpha

    Related Questions to study

    General
    physics-

    The spectrum of a black body at two temperatures 27 ℃ and 327 ℃ is shown in the figure. Let A subscript 1 end subscript and A subscript 2 end subscript be the areas under the two curves respectively. The value of fraction numerator A subscript 2 end subscript over denominator A subscript 1 end subscript end fraction is

    Area under given curve represents emissive power and emissive power proportional to T to the power of 4 end exponent rightwards double arrow A proportional to T to the power of 4 end exponent
    rightwards double arrow fraction numerator A subscript 2 end subscript over denominator A subscript 1 end subscript end fraction equals fraction numerator T subscript 2 end subscript superscript 4 end superscript over denominator T subscript 1 end subscript superscript 4 end superscript end fraction equals fraction numerator open parentheses 273 plus 327 close parentheses to the power of 4 end exponent over denominator open parentheses 273 plus 27 close parentheses to the power of 4 end exponent end fraction equals open parentheses fraction numerator 600 over denominator 300 end fraction close parentheses to the power of 4 end exponent equals fraction numerator 16 over denominator 1 end fraction

    The spectrum of a black body at two temperatures 27 ℃ and 327 ℃ is shown in the figure. Let A subscript 1 end subscript and A subscript 2 end subscript be the areas under the two curves respectively. The value of fraction numerator A subscript 2 end subscript over denominator A subscript 1 end subscript end fraction is

    physics-General
    Area under given curve represents emissive power and emissive power proportional to T to the power of 4 end exponent rightwards double arrow A proportional to T to the power of 4 end exponent
    rightwards double arrow fraction numerator A subscript 2 end subscript over denominator A subscript 1 end subscript end fraction equals fraction numerator T subscript 2 end subscript superscript 4 end superscript over denominator T subscript 1 end subscript superscript 4 end superscript end fraction equals fraction numerator open parentheses 273 plus 327 close parentheses to the power of 4 end exponent over denominator open parentheses 273 plus 27 close parentheses to the power of 4 end exponent end fraction equals open parentheses fraction numerator 600 over denominator 300 end fraction close parentheses to the power of 4 end exponent equals fraction numerator 16 over denominator 1 end fraction
    General
    physics-

    In a vertical U-tube containing a liquid, the two arms are maintained at different temperatures t subscript 1 end subscript and t subscript 2 end subscript. The liquid columns in the two arms have heights l subscript 1 end subscript and l subscript 2 end subscript respectively. The coefficient of volume expansion of the liquid is equal to

    Suppose, height of liquid in each arm before rising the temperature is l.

    With temperature rise height of liquid in each arm increases i. e. blank l subscript 1 end subscript greater than l blank a n d blank l subscript 2 end subscript greater than l
    Also l equals fraction numerator l subscript 1 end subscript over denominator 1 plus gamma t subscript 1 end subscript end fraction equals fraction numerator l subscript 2 end subscript over denominator 1 plus gamma t subscript 2 end subscript end fraction
    rightwards double arrow l subscript 1 end subscript plus gamma l subscript 1 end subscript t subscript 2 end subscript equals l subscript 2 end subscript plus gamma l subscript 2 end subscript t subscript 1 end subscript rightwards double arrow gamma equals fraction numerator l subscript 1 end subscript minus l subscript 2 end subscript over denominator l subscript 2 end subscript t subscript 1 end subscript minus l subscript 1 end subscript t subscript 2 end subscript end fraction

    In a vertical U-tube containing a liquid, the two arms are maintained at different temperatures t subscript 1 end subscript and t subscript 2 end subscript. The liquid columns in the two arms have heights l subscript 1 end subscript and l subscript 2 end subscript respectively. The coefficient of volume expansion of the liquid is equal to

    physics-General
    Suppose, height of liquid in each arm before rising the temperature is l.

    With temperature rise height of liquid in each arm increases i. e. blank l subscript 1 end subscript greater than l blank a n d blank l subscript 2 end subscript greater than l
    Also l equals fraction numerator l subscript 1 end subscript over denominator 1 plus gamma t subscript 1 end subscript end fraction equals fraction numerator l subscript 2 end subscript over denominator 1 plus gamma t subscript 2 end subscript end fraction
    rightwards double arrow l subscript 1 end subscript plus gamma l subscript 1 end subscript t subscript 2 end subscript equals l subscript 2 end subscript plus gamma l subscript 2 end subscript t subscript 1 end subscript rightwards double arrow gamma equals fraction numerator l subscript 1 end subscript minus l subscript 2 end subscript over denominator l subscript 2 end subscript t subscript 1 end subscript minus l subscript 1 end subscript t subscript 2 end subscript end fraction
    General
    physics-

    A bimetallic strip consists of metals X and Y. It is mounted rigidly at the base as shown. The metal X has a higher coefficient of expansion compared to that for metal Y. when bimetallic strip is placed in a cold bath

    The metal X has a higher coefficient of expansion compared to that for metal Y so, on placing bimetallic strip in a cold bath, X will shrink more than Y. Hence, the strip will bend towards the left.

    A bimetallic strip consists of metals X and Y. It is mounted rigidly at the base as shown. The metal X has a higher coefficient of expansion compared to that for metal Y. when bimetallic strip is placed in a cold bath

    physics-General
    The metal X has a higher coefficient of expansion compared to that for metal Y so, on placing bimetallic strip in a cold bath, X will shrink more than Y. Hence, the strip will bend towards the left.
    parallel
    General
    physics-

    The temperature of the two outer surfaces of a composite slab, consisting of two materials having coefficients of thermal conductivity K and 2K and thickness x and 4x, respectively are T subscript 2 end subscript and T subscript 1 end subscript left parenthesis T subscript 2 end subscript greater than T subscript 1 end subscript right parenthesis. The rate of heat transfer through the slab, in a steady state is open parentheses fraction numerator A open parentheses T subscript 2 end subscript minus T subscript 1 end subscript close parentheses K over denominator x end fraction close parentheses f, with f equals to

    Let the temperature of common interface be T ℃. Rate of heat flow
    H equals fraction numerator Q over denominator t end fraction equals blank fraction numerator K A increment T over denominator l end fraction
    therefore H subscript 1 end subscript equals open parentheses fraction numerator Q over denominator t end fraction close parentheses subscript 1 end subscript=fraction numerator 2 K A left parenthesis T minus T subscript 1 right parenthesis end subscript over denominator 4 x end fraction
    And H subscript 2 end subscript equals open parentheses fraction numerator Q over denominator t end fraction close parentheses subscript 2 end subscript=fraction numerator K A left parenthesis T subscript 2 end subscript minus T right parenthesis over denominator x end fraction
    In steady state, the rate of heat flow should be same in whole system i e comma
    H subscript 1 end subscript equals blank H subscript 2 end subscript
    rightwards double arrow fraction numerator 2 K A left parenthesis T minus T subscript 1 end subscript right parenthesis over denominator 4 x end fraction = fraction numerator K A left parenthesis T subscript 2 end subscript minus T right parenthesis over denominator x end fraction
    rightwards double arrow fraction numerator T minus T subscript 1 end subscript over denominator 2 end fraction equals blank T subscript 2 end subscript minus T
    rightwards double arrow T minus T subscript 1 end subscript equals blank 2 T subscript 2 end subscript minus 2 T
    rightwards double arrow T equals fraction numerator 2 T subscript 2 end subscript plus T subscript 1 end subscript over denominator 3 end fraction (i)
    Hence, heat flow from composite slab is
    H equals blank fraction numerator K A left parenthesis T subscript 2 end subscript minus T right parenthesis over denominator x end fraction
    = fraction numerator K A over denominator x end fraction open parentheses T subscript 2 end subscript minus fraction numerator 2 T subscript 2 end subscript plus T subscript 1 end subscript over denominator 3 end fraction close parentheses equals blank fraction numerator K A over denominator 3 x end fraction blank left parenthesis T subscript 2 end subscript minus T subscript 1 end subscript right parenthesis (ii)
    Accordingly, H equals open square brackets fraction numerator A open parentheses T subscript 2 end subscript minus T subscript 1 end subscript close parentheses K over denominator x end fraction close square brackets f (iii)
    By comparing Eqs. (ii) and (iii), we get
    rightwards double arrow f equals blank fraction numerator 1 over denominator 3 end fraction

    The temperature of the two outer surfaces of a composite slab, consisting of two materials having coefficients of thermal conductivity K and 2K and thickness x and 4x, respectively are T subscript 2 end subscript and T subscript 1 end subscript left parenthesis T subscript 2 end subscript greater than T subscript 1 end subscript right parenthesis. The rate of heat transfer through the slab, in a steady state is open parentheses fraction numerator A open parentheses T subscript 2 end subscript minus T subscript 1 end subscript close parentheses K over denominator x end fraction close parentheses f, with f equals to

    physics-General
    Let the temperature of common interface be T ℃. Rate of heat flow
    H equals fraction numerator Q over denominator t end fraction equals blank fraction numerator K A increment T over denominator l end fraction
    therefore H subscript 1 end subscript equals open parentheses fraction numerator Q over denominator t end fraction close parentheses subscript 1 end subscript=fraction numerator 2 K A left parenthesis T minus T subscript 1 right parenthesis end subscript over denominator 4 x end fraction
    And H subscript 2 end subscript equals open parentheses fraction numerator Q over denominator t end fraction close parentheses subscript 2 end subscript=fraction numerator K A left parenthesis T subscript 2 end subscript minus T right parenthesis over denominator x end fraction
    In steady state, the rate of heat flow should be same in whole system i e comma
    H subscript 1 end subscript equals blank H subscript 2 end subscript
    rightwards double arrow fraction numerator 2 K A left parenthesis T minus T subscript 1 end subscript right parenthesis over denominator 4 x end fraction = fraction numerator K A left parenthesis T subscript 2 end subscript minus T right parenthesis over denominator x end fraction
    rightwards double arrow fraction numerator T minus T subscript 1 end subscript over denominator 2 end fraction equals blank T subscript 2 end subscript minus T
    rightwards double arrow T minus T subscript 1 end subscript equals blank 2 T subscript 2 end subscript minus 2 T
    rightwards double arrow T equals fraction numerator 2 T subscript 2 end subscript plus T subscript 1 end subscript over denominator 3 end fraction (i)
    Hence, heat flow from composite slab is
    H equals blank fraction numerator K A left parenthesis T subscript 2 end subscript minus T right parenthesis over denominator x end fraction
    = fraction numerator K A over denominator x end fraction open parentheses T subscript 2 end subscript minus fraction numerator 2 T subscript 2 end subscript plus T subscript 1 end subscript over denominator 3 end fraction close parentheses equals blank fraction numerator K A over denominator 3 x end fraction blank left parenthesis T subscript 2 end subscript minus T subscript 1 end subscript right parenthesis (ii)
    Accordingly, H equals open square brackets fraction numerator A open parentheses T subscript 2 end subscript minus T subscript 1 end subscript close parentheses K over denominator x end fraction close square brackets f (iii)
    By comparing Eqs. (ii) and (iii), we get
    rightwards double arrow f equals blank fraction numerator 1 over denominator 3 end fraction
    General
    physics-

    A solid material is supplied with heat at constant rate and the temperature of the material changes as shown. From the graph, the false conclusion drawn is

    A solid material is supplied with heat at constant rate and the temperature of the material changes as shown. From the graph, the false conclusion drawn is

    physics-General
    General
    physics-

    The energy distribution E with the wavelength left parenthesis lambda right parenthesis for the black body radiation at temperature T blank k e l v i n is shown in the figure. As the temperature is increased the maxima will

    According to Wien’s displacement law lambda subscript m end subscript proportional to fraction numerator 1 over denominator T end fraction. Hence, it temperature increases lambda subscript m end subscript decreases i. e. comma peak of the E minus lambda curve shift towards left

    The energy distribution E with the wavelength left parenthesis lambda right parenthesis for the black body radiation at temperature T blank k e l v i n is shown in the figure. As the temperature is increased the maxima will

    physics-General
    According to Wien’s displacement law lambda subscript m end subscript proportional to fraction numerator 1 over denominator T end fraction. Hence, it temperature increases lambda subscript m end subscript decreases i. e. comma peak of the E minus lambda curve shift towards left
    parallel
    General
    physics-

    A metal rod of length 2 m has cross sectional areas 2 A and A as shown in figure. The ends are maintained at temperatures 100 ℃ and 70 ℃. The temperature at middle point C is

    Let theta be temperature of middle point C and in series rate of heat flow is same
    rightwards double arrow K open parentheses 2 A close parentheses open parentheses 100 minus theta close parentheses equals K A left parenthesis theta minus 70 right parenthesis
    rightwards double arrow 200 minus 2 theta equals theta minus 70 rightwards double arrow 3 theta equals 270 rightwards double arrow theta equals 90 ℃

    A metal rod of length 2 m has cross sectional areas 2 A and A as shown in figure. The ends are maintained at temperatures 100 ℃ and 70 ℃. The temperature at middle point C is

    physics-General
    Let theta be temperature of middle point C and in series rate of heat flow is same
    rightwards double arrow K open parentheses 2 A close parentheses open parentheses 100 minus theta close parentheses equals K A left parenthesis theta minus 70 right parenthesis
    rightwards double arrow 200 minus 2 theta equals theta minus 70 rightwards double arrow 3 theta equals 270 rightwards double arrow theta equals 90 ℃
    General
    physics-

    The coefficient of thermal conductivity of copper is nine times that of steel. In the composite cylindrical bar show in figure, what will be the temperature at the junction of copper ad steel?

    Let the temperature of junction be theta.
    open parentheses fraction numerator increment Q over denominator d subscript 1 end subscript end fraction close parentheses subscript c o p p e r end subscript blank equals open parentheses fraction numerator increment Q over denominator increment T end fraction close parentheses subscript s t e e l end subscript
    K subscript 1 end subscript A equals blank fraction numerator open parentheses 100 minus theta close parentheses over denominator 18 end fraction equals fraction numerator K subscript 2 end subscript A open parentheses theta minus 0 close parentheses over denominator 6 end fraction
    9 K subscript 2 end subscript fraction numerator open parentheses 100 minus theta close parentheses over denominator 3 end fraction equals K subscript 2 end subscript theta
    3theta equals 900 minus 9 theta
    12theta equals 900
    theta equals 75 ℃

    The coefficient of thermal conductivity of copper is nine times that of steel. In the composite cylindrical bar show in figure, what will be the temperature at the junction of copper ad steel?

    physics-General
    Let the temperature of junction be theta.
    open parentheses fraction numerator increment Q over denominator d subscript 1 end subscript end fraction close parentheses subscript c o p p e r end subscript blank equals open parentheses fraction numerator increment Q over denominator increment T end fraction close parentheses subscript s t e e l end subscript
    K subscript 1 end subscript A equals blank fraction numerator open parentheses 100 minus theta close parentheses over denominator 18 end fraction equals fraction numerator K subscript 2 end subscript A open parentheses theta minus 0 close parentheses over denominator 6 end fraction
    9 K subscript 2 end subscript fraction numerator open parentheses 100 minus theta close parentheses over denominator 3 end fraction equals K subscript 2 end subscript theta
    3theta equals 900 minus 9 theta
    12theta equals 900
    theta equals 75 ℃
    General
    Maths-

    Which function is shown in graph?

    Which function is shown in graph?

    Maths-General
    parallel
    General
    Maths-

    Which function is shown in graph?

    Which function is shown in graph?

    Maths-General
    General
    Maths-

    Which function is shown in graph?

    Which function is shown in graph?

    Maths-General
    General
    physics-

    Five rods of same dimensions are arranged as shown in figure. They have thermal conductivities K subscript 1 end subscript comma blank K subscript 2 end subscript comma blank K subscript 3 end subscript comma blank K subscript 4 end subscript a n d K subscript 5 end subscript. When points A blank a n d blank B are maintained at different temperature, no heat would flow through central rod, if

    The equivalent electrical circuit, figure in these cases is of Wheatstone bridge. No current would flow through central rod C D when the bridge is balanced. The condition for balanced Wheatstone bridge is fraction numerator P over denominator Q end fraction equals fraction numerator R over denominator S end fraction (in terms of resistances)
    fraction numerator 1 divided by K subscript 1 end subscript over denominator 1. K subscript 2 end subscript end fraction equals fraction numerator 1 divided by K subscript 3 end subscript over denominator 1 divided by K subscript 4 end subscript end fraction or fraction numerator K subscript 2 end subscript over denominator K subscript 1 end subscript end fraction equals fraction numerator K subscript 4 end subscript over denominator K subscript 3 end subscript end fraction
    Or K subscript 1 end subscript K subscript 4 end subscript equals K subscript 2 end subscript K subscript 3 end subscript

    Five rods of same dimensions are arranged as shown in figure. They have thermal conductivities K subscript 1 end subscript comma blank K subscript 2 end subscript comma blank K subscript 3 end subscript comma blank K subscript 4 end subscript a n d K subscript 5 end subscript. When points A blank a n d blank B are maintained at different temperature, no heat would flow through central rod, if

    physics-General
    The equivalent electrical circuit, figure in these cases is of Wheatstone bridge. No current would flow through central rod C D when the bridge is balanced. The condition for balanced Wheatstone bridge is fraction numerator P over denominator Q end fraction equals fraction numerator R over denominator S end fraction (in terms of resistances)
    fraction numerator 1 divided by K subscript 1 end subscript over denominator 1. K subscript 2 end subscript end fraction equals fraction numerator 1 divided by K subscript 3 end subscript over denominator 1 divided by K subscript 4 end subscript end fraction or fraction numerator K subscript 2 end subscript over denominator K subscript 1 end subscript end fraction equals fraction numerator K subscript 4 end subscript over denominator K subscript 3 end subscript end fraction
    Or K subscript 1 end subscript K subscript 4 end subscript equals K subscript 2 end subscript K subscript 3 end subscript
    parallel
    General
    physics-

    If two metallic plates of equal thicknesses and thermal conductivities K subscript 1 end subscript and K subscript 2 end subscript are put together face to face and a common plate is constructed, then the equivalent thermal conductivity of this plate will be

    In series, R subscript e q end subscript equals R subscript 1 end subscript plus R subscript 2 end subscript rightwards double arrow fraction numerator 2 l over denominator K subscript e q end subscript A end fraction equals fraction numerator l over denominator K subscript 1 end subscript A end fraction plus fraction numerator l over denominator K subscript 2 end subscript A end fraction
    rightwards double arrow fraction numerator 2 over denominator K subscript e q end subscript end fraction equals fraction numerator 1 over denominator K subscript 1 end subscript end fraction plus fraction numerator 1 over denominator K subscript 2 end subscript end fraction rightwards double arrow K subscript e q end subscript equals fraction numerator 2 K subscript 1 end subscript K subscript 2 end subscript over denominator K subscript 1 end subscript plus K subscript 2 end subscript end fraction

    If two metallic plates of equal thicknesses and thermal conductivities K subscript 1 end subscript and K subscript 2 end subscript are put together face to face and a common plate is constructed, then the equivalent thermal conductivity of this plate will be

    physics-General
    In series, R subscript e q end subscript equals R subscript 1 end subscript plus R subscript 2 end subscript rightwards double arrow fraction numerator 2 l over denominator K subscript e q end subscript A end fraction equals fraction numerator l over denominator K subscript 1 end subscript A end fraction plus fraction numerator l over denominator K subscript 2 end subscript A end fraction
    rightwards double arrow fraction numerator 2 over denominator K subscript e q end subscript end fraction equals fraction numerator 1 over denominator K subscript 1 end subscript end fraction plus fraction numerator 1 over denominator K subscript 2 end subscript end fraction rightwards double arrow K subscript e q end subscript equals fraction numerator 2 K subscript 1 end subscript K subscript 2 end subscript over denominator K subscript 1 end subscript plus K subscript 2 end subscript end fraction
    General
    physics-

    The graph, shown in the adjacent diagram, represents the variation of temperature left parenthesis T right parenthesis of two bodies, x and y having same surface area, with time (t) due to the emission of radiation. Find the correct relation between the emissivity and absorptivity power of the two bodies.

    Rate of cooling left parenthesis negative fraction numerator d T over denominator d t end fraction right parenthesis proportional to emissivity(e)
    From the graph,
    open parentheses negative fraction numerator d T over denominator d t end fraction close parentheses subscript x end subscript greater than open parentheses negative fraction numerator d T over denominator d t end fraction close parentheses subscript y end subscript
    therefore e subscript x end subscript greater than e subscript y end subscript
    Further emissivity (e)proportional to absorptive power (a) (good absorbers are good emitters also)
    therefore a subscript x end subscript greater than a subscript y end subscript

    The graph, shown in the adjacent diagram, represents the variation of temperature left parenthesis T right parenthesis of two bodies, x and y having same surface area, with time (t) due to the emission of radiation. Find the correct relation between the emissivity and absorptivity power of the two bodies.

    physics-General
    Rate of cooling left parenthesis negative fraction numerator d T over denominator d t end fraction right parenthesis proportional to emissivity(e)
    From the graph,
    open parentheses negative fraction numerator d T over denominator d t end fraction close parentheses subscript x end subscript greater than open parentheses negative fraction numerator d T over denominator d t end fraction close parentheses subscript y end subscript
    therefore e subscript x end subscript greater than e subscript y end subscript
    Further emissivity (e)proportional to absorptive power (a) (good absorbers are good emitters also)
    therefore a subscript x end subscript greater than a subscript y end subscript
    General
    maths-

    s i n space A plus s i n space 3 A plus s i n space 5 A plus s i n space 7 A equals

    Apply SinC+SinD formula

    s i n space A plus s i n space 3 A plus s i n space 5 A plus s i n space 7 A equals

    maths-General
    Apply SinC+SinD formula
    parallel

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.