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QPages 77-80: Q20: HC Verma: Concepts of Physics - Volume 2 Specific Heat Capacities of Gases Pages 77-80: Q20 Solution: The initial pressure and volume of a given mass of a gas ) are…

The initial pressure and volume of a given mass of a gas Cp/Cv=γC_p/C_v = \gamma) are p0p_0 and V0V_0. The gas can exchange heat with the surrounding. a) It is slowly compressed to a volume V0/2V_0/2 and then suddenly compressed to V0/4V_0/4. Find the final pressure. b) If the gas is suddenly compressed from the volume V0V_0 to V0/2V_0/2 and then slowly compressed to V0/4V_0/4, what will be the final pressure?

Step-by-Step Verified Solution

**Answer:** (a) Pfinal=2γ+1P0P_{final} = 2^{\gamma+1}P_0 (b) Pfinal=2γ+1P0P_{final} = 2^{\gamma+1}P_0. **Step-by-Step Explanation:** Given: initial P0P_0, V0V_0. (a) Isothermal to V0/2V_0/2: P=2P0P = 2P_0. Then adiabatic to V0/4V_0/4: P=2P0×2γ=2γ+1P0P = 2P_0 \times 2^\gamma = 2^{\gamma+1}P_0. (b) Adiabatic to V0/2V_0/2: P=P0×2γP = P_0 \times 2^\gamma. Then isothermal to V0/4V_0/4: P=2γ+1P0P = 2^{\gamma+1}P_0 [citation:16].

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