H calories of heat is required to increase the temperature of one mole of monoatomic gas from 20⁰C to 30⁰C at const. volume. The quantity of heat required to increase the temperature of 2 moles of a diatomic gas from
20⁰C to 25⁰C is at constant volume is

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$\frac{4 H}{3}$

$\frac{5 H}{3}$

2 H

$\frac{7 H}{3}$

answer is B.

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Detailed Solution

For mono atomic gas
$\begin{array}{l} n_{1} = 1 {moled}_{T} = T_{2} - T_{1} = 30 - 20 = 10^{0} C \\ (dQ)_{1} = Hcal \\ C_{v} = \frac{1}{n} \frac{(dQ)_{v}}{dQ} \Rightarrow (dQ)_{v} = {nC}_{v} dT \end{array}$
For monoatomic gas $C_{v} = 3 / 2 R$
$H = 1 \times \frac{3 R}{2} \times 10^{5}; H = 15 R$ .......(1)
For diatomic gas $C_{v} = \frac{5}{2} R$
$\begin{array}{l} (dQ)_{2} = 2 \times \frac{5 R}{2} \times 5 = 25 R . . . . . (2) \\ \frac{(1)}{(2)} = \frac{(dQ)_{2}}{H} = \frac{25 R}{5 R^{'}} = \frac{5 H}{3} \end{array}$