The equation of state 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-o and P-o respectively- The work done by the gas when its temperature doubles isobarically will be dfrac -P-oT-oR-P-o-alpha-dfrac -P-oT-oR-P-o-alpha-P-oT-oRP-oT-oR ln 2

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Toppr Admin · Accepted Answer

Isobaric process means pressure will be constant. For one mole gas, $n = 1$
If $V_{i}$ is the initial volume, $P_{0} V_{i} = R T + α V_{i}, V_{i} = \frac{R T_{0}}{P_{0} - α}$
If $V_{f}$ is the final volume, $P_{0} V_{f} = R .2 T_{0} + α V_{f}, V_{f} = \frac{2 R T_{0}}{P_{0} - α}$
The work done $= \int_{V_{i}}^{V_{f}} P_{0} d V = P_{0} [V_{f} - V_{i}] = \frac{P_{0} R T_{0}}{P_{0} - α}$

Isobaric process means pressure will be constant. For one mole gas, n=1If Vi is the initial volume, P0Vi=RT+αVi,Vi=RT0P0−αIf Vf is the final volume, P0Vf=R.2T0+αVf,Vf=2RT0P0−αThe work done =∫VfViP0dV=P0[Vf−Vi]=P0RT0P0−α