InterviewSolution
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InterviewSolution
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Two samples A and B of the same gas have equal volumes and pressures . The gas is sample A is expanded isothermally to double its volume and the the gas in B is expanded adibatically to double its volume . If the work done by the gas is the same for the two cases, show that gamma satisfies the equation`(1-2 ^(1-gamma)= (gamma - 1 ) 1n2`. |
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Answer» `P_1` = Initial pressure, `V_1` = Initial volume , `P_2` =Final pressure, `V_2`= Final volume Given ,`V_2 = 2V_1` Isothermal work done `=nRT_1l n (V_2)/(V_1)` Adiabatic work done `=(P_1V_1-P_2V_2)/(gamma-1)` Given that work done at both clases are same. Hence, `nRT_1l n = V_2/V_1` `=(P_1V_1-P_2V_2)/(gamma-1)` ...(1) At adiabatic process, `P_2 = P_1(V_2/V_1)^gamma=P_1(1/2)^gamma` From the equation (1) `nRT_1l n2=(P_1V_1(1-1/2^(gamma)2))/(gamma-1)` and `nRT_1 = P_1V_1` So `l n2 = (1-1/2^(gamma)2)/(gamma-1)` or `(gamma-1)l n2=1-2^(1-gamma)` |
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