A gas expands with temperature according to the relation, (V=k T^ 2 / 3 ), where (k ) is a constant. Work done when the temperature changes by (60 ~K ) is ( (R= ) universal gas constant.)

Step-by-step solution

Given, (V=k T^ 2 / 3 ) From definition of work done, ( aligned d W & =P d V= R T V d V & = R T k T^ 2 / 3 d V (i) aligned ) Now, (V=k T^ 2 / 3 ) Taking derivative on the both sides, we get (d V=K 2 3 T^ -1 / 3 d T (ii) ) Substituting the value of Eqs. (ii) in Eqs. (i) and taking integration on the both sides, we get ( aligned W & = 2 3 R _ T₁ ^ T₂ d T= 2 3 R (T₂-T₁ ) & = 2 3 R(60-0)= 2 3 R 60=40 R aligned )