$A$ beaker is filled with water at $4\,^{\circ}C$. At one time the temperature is increased by a few degrees above $4\,^{\circ}C$ and at another time it is decreased by a few degrees below $4\,^{\circ}C$. One shall observe that:

  • A
    the level remains constant in each case
  • B
    in the first case water overflows while in the second case its level comes down
  • C
    in the second case water overflows while in the first case its level comes down
  • D
    water overflows in both the cases

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$A$ cylinder of mass $1\,kg$ is given heat of $20000\,J$ at atmospheric pressure. If the initial temperature of the cylinder is $20\,^oC$,then the work done by the cylinder will be .......$J$. (Given: Specific heat of cylinder $= 400\,J\,kg^{-1}\,^oC^{-1}$,Coefficient of volume expansion $= 9 \times 10^{-5}\,^oC^{-1}$,Atmospheric pressure $= 10^5\,N/m^2$,and density of cylinder $= 9000\,kg/m^3$)

Difficult
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Match List-$I$ with List-$II$.
List-$I$List-$II$
$(A)$ Heat capacity of body$(I)$ $J kg^{-1}$
$(B)$ Specific heat capacity of body$(II)$ $J K^{-1}$
$(C)$ Latent heat$(III)$ $J kg^{-1} K^{-1}$
$(D)$ Thermal conductivity$(IV)$ $J m^{-1} K^{-1} s^{-1}$

Choose the correct answer from the options given below:

The thermo $e.m.f.$ produced in a thermocouple is given by the equation $E = 40\theta - \frac{\theta^2}{20}$,where $\theta$ is the temperature difference between the two junctions. The neutral temperature is ............. $^oC$.

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Two different liquids of same mass are kept in two identical vessels,which are placed in a freezer that extracts heat from them at the same rate,causing each liquid to transform into a solid. The schematic figure below shows the temperature $T$ versus time $t$ plot for the two materials. We denote the specific heat of materials in the liquid (solid) states to be $C_{L1}$ $(C_{S1})$ and $C_{L2}$ $(C_{S2})$,respectively. Choose the correct option given below.

$A$ metal ball immersed in alcohol weighs $W_1$ at $0^{\circ}C$ and $W_2$ at $59^{\circ}C$. The coefficient of cubical expansion of the metal is less than that of alcohol. Assuming that the density of metal is large compared to that of alcohol,it can be shown that

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