Thermodynamics and Thermochemistry 1 Question 9
9. For a diatomic ideal gas in a closed system, which of the following plots does not correctly describe the relation between various thermodynamic quantities? (a)
(c)
(b)
(d)
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Solution:
- For diatomic ideal gases,
$$ C_{V}=\frac{f}{2} R \text { and } C_{p}=\left(\frac{f}{2}+1\right) R $$
where, $f=$ degree of freedom $f=$ translational degree of freedom + rotational degree of freedom
$=3+2=5$ [at normal temperature]
The explanation of various plots are as follows.
(a) We know that, $C_{p}$ is heat capacity at constant pressure. Thus, it does not vary with the variation in pressure. Hence, plot given in option (a) is incorrect.
(b) In this plot, $C_{V}$ first increases slightly with increase in temperature and then increases sharply with temperature. The sharp increase is due to increase in degree of freedom. Thus, plot given in option (b) is correct.
(c) For ideal gases, Internal energy $(U) \propto T$
Thus, as temperature increases internal energy also increases. As temperature increases further degree of freedom also increases thus, there is slight variation in the graph. First translational degree of freedom is present followed by rotational and vibrational degree of freedom. Hence, plot given in option (c) is also correct.
(d) $C_{V}$ is heat capacity at constant volume. Thus, it does not vary with variation in volume. Hence, plot given in option (d) is correct.
