Thermodynamics and Thermochemistry - Result Question 30
30. A monoatomic ideal gas undergoes a process in which the ratio of $p$ to $V$ at any instant is constant and equals to $1$ . What is the molar heat capacity of the gas?
(2006, 3M)
(a) $\dfrac{4 R}{2}$
(b) $\dfrac{3 R}{2}$
(c) $\dfrac{5 R}{2}$
(d) $0$
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Answer:
Correct Answer: 30. (a)
Solution:
Given, $\dfrac{p}{V}=1 \Rightarrow p=V \hspace{6mm}…(i)$
Also from first law : $d q=C _V d T+p d V$
For one mole of an ideal gas : $p V=R T$
$\Rightarrow \hspace{5mm} p d V+V d p =R d T \hspace{6mm}…(ii) $
$\text { From (i) } \hspace{5mm} p d V =V d p$
Substituting in Eq. (ii) gives
$2 p d V =R d T \quad \Rightarrow \quad p d V=\dfrac{R}{2} d T $
$\Rightarrow \quad d q =C _V d T+\dfrac{R}{2} d T $
$\Rightarrow \quad \int \dfrac{d q}{d T} =C _V+\dfrac{R}{2}=\dfrac{3}{2} R+\dfrac{R}{2}=2 R$
BETA
