The volume V of a given mass of monoatomic gas changes with temperature T according to the relation V = K T 2 3 . The workdone when temperature changes by 90 K will be x R . The value of x is [ R universal gas constant ]

Step-by-step solution

We know that work done is W = ∫ P d V             . . . 1 ⇒ P = n R T V               . . . 2 ⇒ W = ∫ n R T V d v             . . . 3 and V = K T 2 / 3         . . . 4 ⇒ W = ∫ n R T K T 2 / 3 · d v           . . . 5 ⇒ from 4   :   d v = 2 3 K T - 1 / 3 d T ⇒ W = ∫ T 1 T 2 n R T K T 2 / 3 2 3   K 1