One mole of an ideal monoatomic gas undergoes two reversible processes (A→B and B → C ) as shown in the given figure:A → B is an adiabatic process. If the total heat absorbed in the entire process ( A → B and B → C ) is RT2ln10, the value of 2 log V3 is ___.[Use, molar heat capacity of the gas at constant pressure,Cp,m=52R ]

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One mole of an ideal monoatomic gas undergoes two reversible processes
( $A \to B$ and B → C ) as shown in the given figure:
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A → B is an adiabatic process. If the total heat absorbed in the entire process
( A → B and B → C ) is ${RT}_{2} \ln 10,$ the value of $2 \log V_{3}$ is ___.
[Use, molar heat capacity of the gas at constant pressure, $C_{p, m} = \frac{5}{2} R$ ]

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answer is 7.

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Detailed Solution

$Q = Q_{AB} + Q_{BC} {RT}_{2} \ln 10 = 0 + (1) {RT}_{2} \ln (\frac{V_{3}}{V_{2}}) \frac{V_{3}}{V_{2}} = 10 A \to B \Rightarrow T . V^{γ - 1} = constant \begin{array}{l} T_{1} V_{1}^{γ - 1} = T_{2} V_{2}^{γ - 1} \\ (600) (10)^{\frac{2}{3}} = (60) {(V_{2})}^{\frac{2}{3}} \\ {(V_{2})}^{\frac{2}{3}} = 10^{\frac{5}{3}} \\ V_{2} = (10)^{\frac{5}{2}} \\ V_{3} = 10 V_{2} \\ V_{3} = (10)^{\frac{7}{2}} \\ 2 \log V_{3} = 7 \end{array}$