One mole of an ideal gas at 900 K , undergoes two reversible processes, I followed by II, as shown below. If the work done by the gas in the two processes are same, the value of ln V 2 V 3 is __

Question

One mole of an ideal gas at 900 K , undergoes two reversible processes, I followed by II, as shown below. If the work done by the gas in the two processes are same, the value of $ln \frac{V _{3}}{V _{2}}$ is $____$ .

( $U$ : internal energy, $S$ : entropy, $p :$ pressure, $V :$ volume, $R :$ gas constant) (Given : molar heat capacity at constant volume, $C_{V, m}$ of the gas is $\frac{5}{2} R$ )

TestHub · Accepted Answer

Δ U I ​ = n C v , m ​ Δ T = W I ​ { q I ​ = 0 } − 1800 R = 1 × 2 5 R ​ × Δ T Δ T = − 720 K W II ​ = W I ​ = − 1800 R = − 1 × R × 180 ln ( V 2 ​ V 3 ​ ​ ) T 2 ​ = 180 K ln ( V 2 ​ V 3 ​ ​ ) = 10

Chemistry - Thermochemistry Question with Solution | TestHub

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