(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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$A$ 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

$A$ copper block of mass $2.5\; kg$ is heated in a furnace to a temperature of $500\; ^{\circ}C$ and then placed on a large ice block. What is the maximum amount of ice (in $kg$) that can melt? (Specific heat of copper $= 0.39\; J\; g^{-1}\; K^{-1}$; heat of fusion of water $= 335\; J\; g^{-1}$)

The height of Victoria Falls is $63 \ m$. What is the difference in temperature of water at the top and at the bottom of the fall? (In $^{\circ}C$)[Given $1 \ cal = 4.2 \ J$ and specific heat of water $= 1 \ cal \ g^{-1} \ ^{\circ}C^{-1}$]

$A$ metal sphere immersed in water weighs $w_1$ at $0^{\circ} C$ and $w_2$ at $50^{\circ} C$. The coefficient of cubical expansion of the metal is less than that of water. Then

Water falls from a height of $500\,m$. The rise in temperature of the water at the bottom,assuming all energy remains in the water,will be ........ $^oC$ [Specific heat of water = $4.2\,kJ/kg\cdot K$]

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 $^{\circ} C$)

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The height of Victoria Falls is $63 \ m$. What is the difference in temperature of water at the top and at the bottom of the fall? (In $^{\circ}C$)
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