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. (c)

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

$$ \frac{3 T^{2}}{V} \cdot d T-\frac{T^{3}}{V^{2}} d V=0 \quad \text { or } \quad 3 d T=\frac{T}{V} \cdot d V \cdots(i) $$

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) $\gamma=\frac{d V}{V \cdot d T}=\frac{3}{T}$



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