show complete solution with explanations if possible.
$For a polytropic process, the formula for the heat (Q) is: \[ \mathrm{Q}=\frac{(\delta-\mathrm{k}) \mathrm{RT}_{1}}{(\delta-1$

For a polytropic process, the formula for the heat (Q) is: \[ \mathrm{Q}=\frac{(\delta-\mathrm{k}) \mathrm{RT}_{1}}{(\delta-1)(\mathrm{k}-1)}\left[\left(\frac{\mathrm{P}_{2}}{\mathrm{P}_{1}}\right)^{\frac{\delta-1}{\delta}}-1\right] \] Derive this using the equation $ \mathrm{dU}=\mathrm{dQ}+\mathrm{dW} $ given that $ \mathrm{PV}^{\delta}=\mathrm{c} $ (constant).

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show complete solution with explanations if possible.
$For a polytropic process, the formula for the heat (Q) is: \[ \mathrm{Q}=\frac{(\delta-\mathrm{k}) \mathrm{RT}_{1}}{(\delta-1$

For a polytropic process, the formula for the heat (Q) is: \[ \mathrm{Q}=\frac{(\delta-\mathrm{k}) \mathrm{RT}_{1}}{(\delta-1)(\mathrm{k}-1)}\left[\left(\frac{\mathrm{P}_{2}}{\mathrm{P}_{1}}\right)^{\frac{\delta-1}{\delta}}-1\right] \] Derive this using the equation $ \mathrm{dU}=\mathrm{dQ}+\mathrm{dW} $ given that $ \mathrm{PV}^{\delta}=\mathrm{c} $ (constant).

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