(A) The change in volume due to thermal expansion is given by $\Delta V_{thermal} = V \alpha \Delta \theta$,where $\Delta \theta$ is the change in tem

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(A) The change in volume due to thermal expansion is given by $\Delta V_{thermal} = V \alpha \Delta \theta$,where $\Delta \theta$ is the change in temperature.The change in volume due to pressure $P$ is given by the definition of bulk modulus: $\beta = -\frac{P}{\Delta V / V}$,which implies $\Delta V_{pressure} = -\frac{PV}{\beta}$.For the cube to regain its original volume,the net change in volume must be zero: $\Delta V_{thermal} + \Delta V_{pressure} = 0$.$V \alpha \Delta \theta - \frac{PV}{\beta} = 0$.$V \alpha \Delta \theta = \frac{PV}{\beta}$.$\Delta \theta = \frac{P}{\alpha \beta}$.

Class 11 Physics 10-1.Thermometry, Thermal Expansion and Calorimetry Mix Examples-Thermometry, Thermal Expansion and Calorimetry

Medium

$A$ cube is subjected to a pressure $P$ on all its faces at a temperature of $0 \, ^\circ C$. By what temperature should the cube be heated so that it regains its original volume? Let the bulk modulus of the cube be $\beta$ and the coefficient of volume expansion be $\alpha$.

A
$\frac{P}{\alpha \beta}$
B
$\frac{P \alpha}{\beta}$
C
$\frac{P \beta}{\alpha}$
D
$\frac{\alpha \beta}{P}$

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10-1.Thermometry, Thermal Expansion and Calorimetry

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Mix Examples-Thermometry, Thermal Expansion and Calorimetry

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MediumJEE MAIN 2022

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Give one example each for solid,liquid,and gas showing expansion with an increase in temperature and contraction with a decrease in temperature.

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$A$ beaker is completely filled with water at $4 \text{ } ^\circ C$. When will the water in this beaker overflow?

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$A$ cube is subjected to a pressure $P$ on all its faces at a temperature of $0 \, ^\circ C$. By what temperature should the cube be heated so that it regains its original volume? Let the bulk modulus of the cube be $\beta$ and the coefficient of volume expansion be $\alpha$.

Similar Questions

Find the difference in temperature between the water at the top and the bottom of a $20 \ m$ high waterfall, assuming $10 \%$ of the energy of the fall is spent in heating the water. [Use specific heat capacity of water $= 4000 \ J \ kg^{-1} K^{-1}$ and $g = 10 \ m/s^2$]. (in $^{\circ} C$)

$A$ thermocouple produces $40 \, \mu V/K$. The temperatures of the cold and hot junctions are $40 \, ^\circ C$ and $20 \, ^\circ C$ respectively. If $150$ such thermocouples are connected in series,what is the total thermo-emf produced in $mV$?

$A$ steam engine intakes $50 \, g$ of steam at $100^{\circ} C$ per minute and cools it down to $20^{\circ} C$. If the latent heat of vaporization of steam is $540 \, cal \, g^{-1}$,then the heat rejected by the steam engine per minute is .........$\times 10^{3} \, cal$.

Give one example each for solid,liquid,and gas showing expansion with an increase in temperature and contraction with a decrease in temperature.

$A$ beaker is completely filled with water at $4 \text{ } ^\circ C$. When will the water in this beaker overflow?

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