Thermodynamics and Thermochemistry 1 Question 1
1. An ideal gas is allowed to expand from $1 \mathrm{~L}$ to $10 \mathrm{~L}$ against a constant external pressure of 1 bar. The work done in $\mathrm{kJ}$ is
(2019 Main, 12 April I)
(a) -9.0
(b) +10.0
(c) -0.9
(d) -2.0
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Solution:
- Key Idea Work done during isothermal expansion of an ideal gas is given by the equation.
$$ W=-p_{\text {ext }}\left(V_{2}-V_{1}\right) $$
According to the given conditions, the expansion is against constant external pressure. So, the work done is given by following formula;
$$ \begin{aligned} W & =-p_{\text {ext }}\left(V_{2}-V_{1}\right) \ & =-1 \text { bar }(10 \mathrm{~L}-1 \mathrm{~L})=-9 \mathrm{~L} \text { bar } \quad(\because 1 \mathrm{Lbar}=100 \mathrm{~J}) \ & =-9 \times 100 \mathrm{~J}=-0.9 \mathrm{~kJ} \end{aligned} $$
