Question

A gas expands with temperature according to the relation

V = KT2/3. Work done when the temperature changes by 60 K is

• A. 10 R
• B. 30 R
• C. 40 R
• D. 20 R

Answer 1

Answer: (C)

40 R

Answer 2

: Here,

Given

$\therefore \frac { d V } { V } = \frac { K \frac { 2 } { 3 } T ^ { - 1 / 3 } d T } { K T ^ { 2 / 3 } } = \frac { 2 } { 3 } \frac { d T } { T } \ldots . . ( i i )$

Form (i) $W = \int _ { T _ { 1 } } ^ { T _ { 2 } } R T \frac { d V } { V }$

$= \int _ { T _ { 1 } } ^ { T _ { 2 } } R T \frac { 2 } { 3 } \frac { d T } { T } ( u \sin g ( i i ) )$

$\therefore W = \frac { 2 } { 3 } R \left( T _ { 2 } - T _ { 1 } \right) = \frac { 2 } { 3 } R \times 60 = 40 R$