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  • One mole of an ideal gas requires 207 J heat to raise its temperature by 10 K when heated at constant pressure. If the same gas is heated at constant volume to raise the temperature by the same 10

One mole of an ideal gas requires 207 J heat to raise its temperature by 10 K when heated at constant pressure. If the same gas is heated at constant volume to raise the temperature by the same 10 K, the heat required will be ( R, the gas constant = \left.8.3 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}\right)

Option: 1

198.7 J


Option: 2

29 J


Option: 3

215.3 J


Option: 4

124 J


Answers (1)

best_answer

Heat energy required to raise the temperature of n moles of a gas by ?T at constant
pressure is

\mathrm{Q_p=n C_p \Delta t}

Heat energy required to raise the temperature n moles of a gas by ?T at constant
volume is

\mathrm{\begin{aligned} & Q_v=n C_v \Delta T, \therefore \frac{Q_v}{Q_p}=\frac{C_v}{C_p} \\ & \text { Or } Q_v=\frac{C_v}{C_p} \times Q_p=\frac{3 R / 2}{3 R / 2} \times Q_p \\ & =\frac{3}{5} \times 207=124.2=124 \mathrm{~J} \end{aligned}}

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Rishabh

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