First slide

Law of equipartition of energy

Question

15 Joule of heat is supplied to a given amount of hydrogen gas at constant volume and its temperature is raised by $5^{o} C$ . What amount of heat should be supplied to the same gas at constant pressure to raise its temperature by $5^{o} C$ ?

Moderate

A

18 Joule
B

21 Joule
C

28 Joule
D

25 Joule

Solution

f = number of degrees of freedom of the molecules of hydrogen gas = 3+2=5.
$∴ C_{V} = \frac{f R}{2} = \frac{5 R}{2} and C_{P} = (\frac{f + 2}{2}) R = \frac{7}{2} R$
$∴ \frac{Q_{P}}{Q_{V}} = \frac{n . C_{P} . Δ T}{n . C_{V} . Δ T} = \frac{C_{P}}{C_{V}} = \frac{7}{5}$
$\Rightarrow Q_{P} = \frac{7}{5} \times 15 J = 21 Joule$

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