In an adiabatic expansion of a gas, the initi | vedclass

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Question

(C) The change in internal energy $(\Delta U)$ of an ideal gas depends only on the change in temperature and is given by the formula: $\Delta U = nC_v

Vedclass · Accepted Answer

$\frac{nR}{\gamma-1}(T_2-T_1)$

Vedclass · Answer

(C) The change in internal energy $(\Delta U)$ of an ideal gas depends only on the change in temperature and is given by the formula: $\Delta U = nC_v\Delta T$. For an ideal gas, the molar heat capacity at constant volume is $C_v = \frac{R}{\gamma-1}$. Substituting this into the internal energy formula, we get: $\Delta U = n \left(\frac{R}{\gamma-1}\right) (T_2 - T_1)$. Therefore, the change in internal energy is $\frac{nR}{\gamma-1}(T_2 - T_1)$.

In an adiabatic expansion of a gas, the initial and final temperatures are $T_1$ and $T_2$ respectively. Then, the change in internal energy of the gas is:
$[R = \text{gas constant}, \gamma = \text{adiabatic ratio}]$

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