Question

Pressure P, volume V and temperature T for a certain gas are related by P = , where A and B are constants. The work done by the gas as its temperature change from T1 to T2 while pressure remaining constant is

• A. A – (T2 – T1)
• B. A(T2 – T1) – B(T22 – T12)
• C. (T22 – T12) – (T23 – T13)
• D. A(T2 – T1)2 – (T2 – T1)3

Answer 1

Answer: (B)

A(T2 – T1) – B(T22 – T12)

Answer 2

: here $P = \frac { A T - B T ^ { 2 } } { V }$Or $P V = A T - B T ^ { 2 }$

Since p is a constant

Work done = pdV

$\therefore W = \int _ { T _ { 1 } } ^ { T _ { 2 } } ( A - 2 B T ) d T = \left[ A T - B T ^ { 2 } \right] _ { T _ { 1 } } ^ { T _ { 2 } } ( u \sin g ( i ) )$

$= A \left( T _ { 2 } - T _ { 1 } \right) - B \left( T _ { 2 } ^ { 2 } - T _ { 1 } ^ { 2 } \right)$