P-V diagram of 2,g of He gas for A to B proce | vedclass

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Question

$W=$ Area $=\frac{1}{2}\left(P_{0}+2 P_{0}\right) \cdot\left(2 V_{0}-V_{0}\right)=+\frac{3 P_{0} V_{0}}{2}$

$\mathrm{P}_{0} \mathrm{V}_{0}=\mu \mat

Vedclass · Accepted Answer

$6\,P_0V_0$

Vedclass · Answer

$W=$ Area $=\frac{1}{2}\left(P_{0}+2 P_{0}ight) \cdot\left(2 V_{0}-V_{0}ight)=+\frac{3 P_{0} V_{0}}{2}$

$\mathrm{P}_{0} \mathrm{V}_{0}=\mu \mathrm{RT}_{1} \quad$ and       $\left(2 \mathrm{P}_{0}ight)\left(2 \mathrm{V}_{0}ight)=\mu \mathrm{R} \mathrm{T}_{2}$

On subtracting $3 \mathrm{P}_{0} \mathrm{V}_{0}=\mu \mathrm{R} \Delta \mathrm{T}$

Now $\quad \Delta \mathrm{U}=\mu \mathrm{C}_{\mathrm{v}} \Delta \mathrm{T}=\mu\left(\frac{3}{2} \mathrm{R}ight) 	imes\left[\mathrm{T}_{2}-\mathrm{T}_{1}ight]$

$\Rightarrow \quad \frac{3}{2}(\mu R \Delta T)=\frac{9 P_{0} V_{0}}{2}$

$\mathrm{Q}=\mathrm{W}+\Delta \mathrm{U}=\frac{3 \mathrm{P}_{0} \mathrm{V}}{2}+\frac{9 \mathrm{P}_{0} \mathrm{V}_{0}}{2}=6 \mathrm{P}_{0} \mathrm{V}_{0}$

$P-V$ diagram of $2\,g$ of $He$ gas for $A \to B$ process is shown. What is the heat given to the gas ?

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