Heat and Thermodynamics 6 Question 6
10. An ideal gas is expanding such that $p T^{2}=$ constant. The coefficient of volume expansion of the gas is
$(2008,3 M)$
(a) $\frac{1}{T}$
(b) $\frac{2}{T}$
(c) $\frac{3}{T}$
(d) $\frac{4}{T}$
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Answer:
Correct Answer: 10. (a)
Solution:
10.. $p T^{2}=$ constant
$\therefore \quad\left(\frac{n R T}{V}\right) T^{2}=$ constant or $T^{3} V^{-1}=$ constant
Differentiating the equation, we get
$$ \frac{3 T^{2}}{V} \cdot d T-\frac{T^{3}}{V^{2}} d V=0 \quad \text { or } \quad 3 d T=\frac{T}{V} \cdot d V $$
From the equation
$$ d V=V \gamma d T $$
$\gamma=$ coefficient of volume expansion of gas $=\frac{d V}{V \cdot d T}$
From Eq. (i) $\gamma=\frac{d V}{V \cdot d T}=\frac{3}{T}$
