A sample of gas at temperature T is adiabatically expanded to double its volume. The work done by the gas in the process is ( C _ P C _ V = = 3 2 )( R = gas constant )

Step-by-step solution

Using the formula for adiabatic expansion, aligned & T ₁ ~V ₁^ -1 = T ₂ ~V ₂^ -1 & ~T ₁ ~V ₁^ (1 / 2) = T ₂ (2 ~V ₁^ 1 / 2 ) . ( Given: = 3 2 ) & T ₁= T ₂( 2 ) & T ₂= T 2 aligned Work done aligned W _ adi = & R ( T - T ₂ ) -1 = R ( T - T 2 ) 1 2 & = R ( 2 ~T - T ) 2 2= RT ( 2 -1) 2 W _ adi & = RT (2- 2 ) aligned