In an adiabatic process, the state of a gas is changed from \(P_1, V_1, T_1\) to \(P_2, V_2, T_2\). Which of…

In an adiabatic process, the state of a gas is changed from \(P_1, V_1, T_1\) to \(P_2, V_2, T_2\). Which of the following relations is correct?
  1. \(T_1 V_1^{\gamma-1}=T_2 V_2^{\gamma-1}\)
  2. \(P_1 V_1^{\gamma-1}=P_2 V_2^{\gamma-1}\)
  3. \(T_1 P_1^\gamma=T_2 P_2^\gamma\)
  4. \(T_1 V_1^\gamma=T_2 V_2^\gamma\)

Solution

Adiabatic relation between \(T\) and \(V\) is \(\begin{aligned} & T V_1^{\gamma-1}=\text { constant } \\ & \therefore \quad T_1 V_1^{\gamma-1}=T_2 V_2^{\gamma-1} \end{aligned}\)

Asked in: MHT CET 2022 (11 Aug Shift 1)

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