Heat and Thermodynamics 4 Question 1
1. A diatomic gas with rigid molecules does $10 J$ of work when expanded at constant pressure. What would be the heat energy absorbed by the gas, in this process?
(2019 Main, 12 April II)
(a) $25 J$
(b) $35 J$
(c) $30 J$
(d) $40 J$
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Answer:
Correct Answer: 1. (b)
Solution:
- Work done by a gas is
$$ W=p \Delta V=n R \Delta T=10 J \quad (given) \cdots(i) $$
As the gas is diatomic,
$C _p=$ specific heat of gas at constant pressure $=\frac{7}{2} R$
So, heat absorbed by gas at constant pressure is
$$ \begin{aligned} \Delta Q & =n C _p \Delta T=n \frac{7}{2} R \Delta T \\ & =\frac{7}{2}(n R \Delta T) \\ & =\frac{7}{2} \times 10 \quad [From Eq. (i)]\\ & =35 J \end{aligned} $$
