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The equation of state for a gas is given by $\;PV=nRT+ \alpha V\;$ ,where n is the number of moles and $\;\alpha\;$ is a positive constant . The initial temperature and pressure of one mole of the gas contained in a cylinder are $\;T_{0}\;$ and $\;P_{0}\;$ respectively . The work done by the gas when its temperature doubles isobarically will be :

$(a)\;\large\frac{P_{0}T_{0}R}{P_{0} -\alpha} \qquad(b)\;\large\frac{P_{0}T_{0}R}{P_{0} +\alpha} \qquad(c)\;\normalsize P_{0}T_{0}R \;ln 2 \qquad(d)\;\normalsize P_{0}T_{0}$

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