An ideal gas at pressure P and volume V is ex | vedclass

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Question

$\mathrm{V}_{\mathrm{i}}=\mathrm{V} \quad \mathrm{V}_{\mathrm{f}}=2 \mathrm{V}$

$P_{i}=P$

$(P) \rightarrow(y)$ isobaric process

$\mathrm{W}=\

Vedclass · Accepted Answer

$p-y, q-z, r-x$

Vedclass · Answer

$\mathrm{V}_{\mathrm{i}}=\mathrm{V} \quad \mathrm{V}_{\mathrm{f}}=2 \mathrm{V}$

$P_{i}=P$

$(P) \rightarrow(y)$ isobaric process

$\mathrm{W}=\mathrm{P} \Delta \mathrm{V}=\mathrm{PV}$

$(q) \rightarrow(z)$ isothermal

$\mathrm{W}=\mathrm{nRT} \ln \frac{\mathrm{V}_{\mathrm{f}}}{\mathrm{V}_{\mathrm{i}}}=\mathrm{PV} \ln 2$

$(r) \rightarrow(x)$ Adiabatic

$P_{f}=\left(\frac{V_{i}}{V_{f}}\right)^{\gamma} P_{i}=2^{\gamma} P$

$W=\frac{P_{f} V_{f}-P_{i} V_{i}}{1-\gamma}=\frac{\left(2^{-\gamma} P\right)(2 V)-P V}{1-\gamma}$

$\Rightarrow w=\frac{P V\left(1-2^{1-\gamma}\right)}{\gamma-1}$

Column $I$	Column $II$
$(p)$ isobaric	$(x)$ $\frac{{PV(1 - {2^{1 - \gamma }})}}{{\gamma - 1}}$
$(q)$ isothermal	$(y)$ $PV$
$(r)$ adiabatic	(z) $PV\,\iota n\,2$

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