Question

A gas container as shown in figure has a piston-spring arrangement. The initial volume of gas is $0.5m^3$. Pressure inside the cylinder is 200 kPa. Initially there is no spring force gas is heated to increase the volume by 2 times and final pressure is 600 kPa. Take extension to be linear. What percentage of work is done against the spring?

• A. 75%
• B. 100%
• C. 25%
• D. 50%

Answer 1

The correct option is D 50%

For linear relationship the $p-V$ diagram for process in given

$\text{Area (1) = work done against spring}$

$\text{Area (2) = work done against atmosphere and weight of piston.}$

$\Rightarrow \text{Area (1) =}\frac{1}{2}\times (1-0.5)\times 400=100kJ$

$\text{Area (2) =}200\times (1-0.5)=100kJ$

$\Rightarrow \text{\% of work against spring =}\frac{\text{Area(1)}}{\text{Area(1)+Area(2)}}\times 100=50\text{\%}$