Question
Figure. shows three paths through which a gas can be taken from the state A to the state B. Calculate the work done by the gas in each of the three paths.
✓
Answer
In path ACB,
$W_{A C}+W_{B C}=0+p d v=30 \times 10^3(25-10) \times 10^{-6}=0.45 \mathrm{~J}$
In path $A B, W_{A B}=\frac{1}{2} \times(10+30) \times 10^3 \times 15 \times 10^{-6}=0.30 \mathrm{~J}$
In path $ A D B, W=W_{A D}+W_{D B}=10 \times 10^3(25-10) \times 10^{-6}+0=0.15 \mathrm{~J}$
$W_{A C}+W_{B C}=0+p d v=30 \times 10^3(25-10) \times 10^{-6}=0.45 \mathrm{~J}$
In path $A B, W_{A B}=\frac{1}{2} \times(10+30) \times 10^3 \times 15 \times 10^{-6}=0.30 \mathrm{~J}$
In path $ A D B, W=W_{A D}+W_{D B}=10 \times 10^3(25-10) \times 10^{-6}+0=0.15 \mathrm{~J}$
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