Question 187: Thermodynamics & KTG

Question

An ideal gas exists in a state with pressure $P_0$, volume $V_0$. It is isothermally expanded to 4 times of its initial volume $\left(\mathrm{V}_0\right)$, then isobarically compressed to its original volume. Finally the system is heated isochorically to bring it to its initial state. The amount of heat exchanged in this process is

Accepted Answer

$$\begin{aligned}
& \omega_1=\mathrm{P}_0 \mathrm{v}_0 \ell \mathrm{n} 4 \
& \omega_2=\frac{\mathrm{P}_0}{4}\left(-3 \mathrm{v}_0ight)=-\frac{3 \mathrm{P}_0 \mathrm{v}_0}{4} \
& \omega_3=0 \
& \mathrm{Q}_{\mathrm{T}}=\Delta \mathrm{U}_{	ext {cyclic }}+\omega \
& \mathrm{Q}_{\mathrm{T}}=\omega \quad\left(\Delta \mathrm{U}_{	ext {cyclic }}=0ight) \
& \mathrm{Q}_{\mathrm{T}}=\mathrm{P}_0 \mathrm{v}_0\left(\ln 4-\frac{3}{4}ight) \
& =\mathrm{P}_0 \mathrm{v}_0(2 \ln 2-0.75)
\end{aligned}$$

Answer

$\mathrm{P}_0 \mathrm{~V}_0(\ln 2-0.75)$

Answer

$\mathrm{P}_0 \mathrm{~V}_0(2 \ln 2-0.75)$

Answer

$\mathrm{P}_0 \mathrm{~V}_0(2 \ln 2-0.25)$

Answer

$\mathrm{P}_0 \mathrm{~V}_0(\ln 2-0.25)$

Thermodynamics & KTG

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