An ideal gas undergoes isothermal compression from 5 m³ against a constant external pressure of 4 Nm^-2 . Heat released in this process is used to increase the temperature of 1 mole of A/. If molar heat capacity of A/ is $24 J m o l^{- 1} K^{- 1}$ the temperature of A/ increases by

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$\frac{3}{2} K$

$\frac{2}{3} K$

$1 K$

answer is B.

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Detailed Solution

Work done on isothermal irreversible for ideal gas

$\begin{array}{l} = - P_{ex} (V_{2} - V_{1}) \\ = - 4 N / m^{2} (1 m^{3} - 5 m^{3}) = 16 Nm \end{array}$

Isothermal process ideal gas

$\begin{array}{l} Δ U = 0 \\ q = - w \\ = - 16 Nm \\ = - 16 J \end{array}$

Heat used to increase temperature of AI

$\begin{array}{l} q = n C_{m} Δ T \\ 16 J = 1 \times 24 \frac{J}{m o l . K} \times Δ T \Rightarrow Δ T = \frac{2}{3} K . \end{array}$

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