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When Q amount of heat is supplied to 2 moles of a mono atomic gas at constant volume its temperature increases by $20^{o} C$ . What will be the change in temperature of 4 moles of a diatomic ideal gas when 2Q amount of heat is supplied to it at constant volume?

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$30^{o} C$

$10^{o} C$

$12^{o} C$

$15^{o} C$

answer is C.

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Detailed Solution

$Q = n . c_{v} . ∆ T = n . \frac{R}{(γ - 1)} . ∆ T$

$∴ \frac{Q_{2}}{Q_{1}} = (\frac{n_{2}}{n_{1}}) (\frac{γ_{1} - 1}{γ_{2} - 1}) (\frac{∆ T_{2}}{∆ T_{1}})$

For mono atomic gas , $γ_{1} = \frac{3 + 2}{3} = \frac{5}{3}$

For diatomic gas, $γ_{2} = \frac{5 + 2}{5} = \frac{7}{5}$

$∴ \frac{2 Q}{Q} = (\frac{4}{2}) \frac{(\frac{5}{3} - 1)}{(\frac{7}{5} - 1)} . \frac{∆ T_{2}}{20} \Rightarrow 2 = 2 (\frac{2}{3} . \frac{5}{2}) . \frac{∆ T_{2}}{20} \Rightarrow ∆ T_{2} = 12^{o} C$

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