One mole of an ideal gas is kept enclosed under a light piston (area \( =10^{-2} \mathrm{~m}^{2}...

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One mole of an ideal gas is kept enclosed under a light piston (area \( =10^{-2} \mathrm{~m}^{2} \) ) connected by a compressed spring (spring constant \( 100 \mathrm{~N} / \mathrm{m} \) ). The volume of gas is \( 0.83 \mathrm{~m}^{3} \) and its temperature is \( 100 \mathrm{~K} \). The gas is heated so that it compresses the spring further by \( 0.1 \mathrm{~m} \). The work done by the gas in the process is (Take \( R=8.3 \mathrm{~J} / \) mole and suppose there is no atmosphere) :
(a) \( 3 \mathrm{~J} \)
(b) \( 6 \mathrm{~J} \)
(c) \( 9 \mathrm{~J} \)
(d) \( 1.5 \mathrm{~J} \)
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