One mole of an ideal gas is taken from a to b along two paths denoted by the solid and the dashed lines as shown in the graph below. If the work done along the solid line path is W s and that along

Question

One mole of an ideal gas is taken from a to b along two paths denoted by the solid and the dashed lines as shown in the graph below. If the work done along the solid line path is W s ​ and that along the dotted line path is W d ​ , then the integer closest to the ratio W s ​ W d ​ ​ is

TestHub · Accepted Answer

Solid line represents reversible isothermal process.
So, work $W_{s} = - 4 \times 0.5 ln (\frac{5.5}{0.5}) = - 2 ln 11 L - atm$ Dotted line represents irreversible process So, work $W_{d} = - {4 \times 1.5 + 1 \times 1 + \frac{2}{3} \times 2.5} = - {6 + 1 + \frac{5}{3}} L - atm = - \frac{26}{3} L - atm$ So $\frac{W _{d}}{W _{s}} = \frac{26}{3 \times 2 l n 11} \approx 2$ Energetics Conceptual III

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