The amount of work done in an adiabatic expan | vedclass

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(B) For an adiabatic process,the work done $W$ by an ideal gas is given by the first law of thermodynamics: $Q = \Delta U + W$. Since the process is a

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$\frac{R}{{\gamma - 1}}(T - {T_1})$

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(B) For an adiabatic process,the work done $W$ by an ideal gas is given by the first law of thermodynamics: $Q = \Delta U + W$. Since the process is adiabatic,$Q = 0$,so $W = -\Delta U$.For an ideal gas,the change in internal energy is $\Delta U = nC_v \Delta T$. For $1 	ext{ mole}$ of gas,$n = 1$ and $C_v = \frac{R}{\gamma - 1}$.Thus,$W = -[C_v(T_1 - T)] = -[\frac{R}{\gamma - 1}(T_1 - T)]$.Simplifying this,we get $W = \frac{R}{\gamma - 1}(T - T_1)$.

The amount of work done in an adiabatic expansion from temperature $T$ to ${T_1}$ is

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