3 moles of a diatomic gas are taken at temperature T. Its volume is varied according to the law V = α T − 2 ( α is a positive constant during the process). The final temperature of the gas is found to

Question

3 moles of a diatomic gas are taken at temperature T. Its volume is varied according to the law V = α T − 2 ( α is a positive constant during the process). The final temperature of the gas is found to be 2T. The heat supplied to the gas is

TestHub · Accepted Answer

V T 2 = α and T = n R P V ​ give P 2 V 3 = α n 2 R 2 , i.e. P V 3/2 = const (polytropic index m = 2 3 ​ ). C = C v ​ − m − 1 R ​ = 2 5 ​ R − 2 3 ​ − 1 R ​ = 2 R ​ . Q = n C Δ T = 3 × 2 R ​ × ( 2 T − T ) = 2 3 ​ RT .

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