Thermodynamics and Thermochemistry 1 Question 61
64. 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 $W_{d} / W_{s}$ is
(2010)
Subjective Questions
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Solution:
- Work done along dashed path $|-W|=\Sigma p \Delta V$
$$ =4 \times 1.5+1 \times 1+\frac{2}{3} \times 2.5=8.65 \mathrm{~L} \mathrm{~atm} $$
Work done along solid path $-W=n R T \ln \frac{V_{2}}{V_{1}}=p_{1} V_{1} \ln \frac{V_{2}}{V_{1}}$
$$ =2 \times 2.3 \log \frac{5.5}{0.5}=2 \times 2.3 \log 11=4.79 $$
$$ \Rightarrow \quad \frac{W_{d}}{W_{s}}=\frac{8.65}{4.79}=1.80 \approx 2 $$
