(D) For an ideal gas,the internal energy $U$ is given by $U = \frac{n R T}{\gamma-1}$.Since $n = 1$ mole,$U = \frac{R T}{\gamma-1}$.From the ideal gas

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(D) For an ideal gas,the internal energy $U$ is given by $U = \frac{n R T}{\gamma-1}$.Since $n = 1$ mole,$U = \frac{R T}{\gamma-1}$.From the ideal gas law,$p V = R T$,so $U = \frac{p V}{\gamma-1}$.The change in internal energy $\Delta U$ is given by $\Delta U = U_f - U_i$.Initial state: $p V_i = p V$,so $U_i = \frac{p V}{\gamma-1}$.Final state: $p V_f = p(2V) = 2 p V$,so $U_f = \frac{2 p V}{\gamma-1}$.Therefore,$\Delta U = \frac{2 p V}{\gamma-1} - \frac{p V}{\gamma-1} = \frac{p V}{\gamma-1}$.

Class 11 Physics Thermodynamics First Law of Thermodynamics

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The volume of one mole of the gas is changed from $V$ to $2V$ at constant pressure $p$. If $\gamma$ is the ratio of specific heats of the gas,what is the change in internal energy of the gas?

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A
$\frac{R p V}{\gamma-1}$
B
$\frac{R}{\gamma-1}$
C
$p V$
D
$\frac{p V}{\gamma-1}$

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The volume of one mole of the gas is changed from $V$ to $2V$ at constant pressure $p$. If $\gamma$ is the ratio of specific heats of the gas,what is the change in internal energy of the gas?

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Assertion : Heat and work are modes of energy transfer to a system resulting in change in its internal energy.
Reason : Heat and work in thermodynamics are state variables.
The correct option among the following is