Fundamentals of thermodynamics

Question

One mole of an ideal gas is heated at constant pressure from 0°C to 100°C. If the gas were expanded isothermally and reversibly at O°C from 1 atm to some other pressure P_{t }what must be the final pressure if the maximum work is equal to the work involved in (a)?

Moderate

Solution

Now the work equivalent to 198.7 cal is used up in causing reversible isothermal expansion of gas at 0°C, then

$\begin{array}{l}{W}_{\mathrm{R}}=-2.303nRT{\mathrm{log}}_{10}\frac{{P}_{1}}{{P}_{2}}\\ \therefore -198.7=-2.303\times 1\times 1.987\times 273{\mathrm{log}}_{10}\frac{1}{{P}_{t}}\\ \therefore {P}_{t}=0.694\mathrm{atm}\end{array}$

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