Cylinder fitted with a spring loaded piston shown in figure contains $0.01 m^{3}$ gas at a pressure of $10^{5} P a .$ The cross-sectional area of the piston is $0.05 m^{2}$ Initially the spring does not touch the piston but atmospheric pressure of $10^{5} P a$ acts on the piston. The gas is slowly heated till the volume is increased to three times the original value. If the force constant of the spring is 25kN/m calculate the work done (in joule ) by the gas.

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Detailed Solution

$W_{g a s} + W_{s p r i n g} + W_{a t m} = 0 W_{g a s} - \frac{1}{2} \times 25 \times 10^{3} \times {(0.2)}^{2} - 10^{5} \times 0.05 \times 0.4 = 0 W_{g a s} = 2500 J = 2.5 k J$

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