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# A gas with $\large\frac {C_p}{C_v} = \gamma$ goes from an initial state of $(P_1,V_1,T_1)$ to a final state of $(P_2,V_2,T_2)$ through an adiabatic process. The work done by the gas is?

$(A) \; \large\frac{nR (T_1-T_2)}{\gamma-1}$ $(B) \; \gamma \large\frac{(P_1V_1+P_2V_2) (T_1-T_2)}{\gamma-1}$ $(C) \; \gamma \large\frac{(P_1V_1+P_2V_2)}{\gamma-1}$ $(D) \; \large\frac{n\gamma R (T_1-T_2)}{\gamma-1}$

$\Delta Q = \Delta u + \Delta w$
$\Delta Q = 0$ for an adiabatic process.
So, $\Delta w = - \Delta u = - \large\frac{nfR(T_2-T_1)}{2}$$= \large\frac{nR}{\gamma-1}$${T_1-T_2}$ (Substituting $\;f = \large\frac{2}{\gamma-1}$)
edited Aug 9, 2014