Question

Which of the following relation is correct regarding one mole of an ideal gas for adiabatic reversible process?

• A. $ln\frac{T_{2}}{T_{1}}=\frac{R}{C_{V}}ln\frac{V_{2}}{V_{1}}$
• B. $ln\frac{T_{2}}{T_{1}}=\frac{R}{C_{P}}ln\frac{P_{1}}{P_{2}}$
• C. $ln\frac{T_{2}}{T_{1}}=\frac{R}{C_{P}}ln\frac{P_{2}}{P_{1}}$
• D. $\frac{R}{C_{V}}ln\frac{V_{1}}{ V_{2}}=\frac{R}{C_{P}}ln\frac{P_{1}}{P_{2}}$

Answer 1

Answer: (C)

For adiabatic process
$\frac{T_{2}}{ T_{1}}=\left(\frac{V_{1}}{ V_{2}}\right)^{\gamma - 1}=\left(\frac{P_{1}}{P_{2}}\right)^{\frac{1 - \gamma }{\gamma }}$
$\Rightarrow \frac{T_{2}}{ T_{1}}=\left(\frac{V_{1}}{ V_{2}}\right)^{\frac{R}{C_{v}}}=\left(\frac{P_{2}}{P_{1}}\right)^{\frac{R}{C_{P}}}$
or $ln\frac{T_{2}}{ T_{1}}=\frac{R}{C_{v}}ln\frac{V_{1}}{ V_{2}}=\frac{R}{C_{P}}ln\frac{P_{2}}{P_{1}}$