A sample of 1 mole gas at temperature T is adiabatically expanded to double its volume. If adiabatic constant for the gas is γ = 2 3 , then the work done by the gas in the process is:

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A sample of 1 mole gas at temperature T is adiabatically expanded to double its volume. If adiabatic constant for the gas is γ = 2 3 ​ , then the work done by the gas in the process is:

TestHub · Accepted Answer

​ TV γ − 1 = constant ⇒ T ( V ) 2 3 ​ − 1 = T f ​ ( 2 V ) 2 3 ​ − 1 ⇒ TV 2 1 ​ = T f ​ ( 2 ) 2 1 ​ ( V ) 2 1 ​ ⇒ T f ​ = ( 2 ​ T ​ ) Now, W.D. = 1 − γ nR Δ T ​ = 1 − 2 3 ​ 1 ⋅ R [ 2 ​ T ​ − T ] ​ ⇒ W.D. = 2 RT [ 1 − 2 ​ 1 ​ ] ⇒ W.D. = RT [ 2 − 2 ​ ] ​

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