An ideal gas undergoes the process $1 \rightarrow 2$ as shown in the figure, the heat supplied and work done in the process is $\Delta \,\,Q$ and $\Delta \,\,W$ respectively. The ratio $\Delta \,\,Q :$ $\Delta \,\,W$ is
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$\Rightarrow \triangle \omega=\triangle Q-\triangle U$
$\Delta Q=C_{P}^{n} \Delta T$
$\Delta U= C_{v}^{n} \Delta T$
$\Delta \omega=n\left(C_{P}-C_{N}\right) \Delta T$
$\triangle Q: \triangle \omega$
$\frac{C_{P}}{C_{V}}=\gamma,=\frac{C_{P}}{C_{P}-C_{V}}$
$=\frac{C_{P} / C_{V}}{C_{P} / C_{V}-1}=\frac{\gamma}{\gamma-1}$
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