One mole of oxygen is contained in a rigid container with walls of inner surface area A, thickness d and thermal conductivity K. The gas is at initial temperature T 0 and the surrounding temperature

Question

One mole of oxygen is contained in a rigid container with walls of inner surface area A, thickness d and thermal conductivity K. The gas is at initial temperature T 0 ​ and the surrounding temperature of air is 2 T 0 ​ . The temperature of the gas at time t is (R is gas constant) :-

TestHub · Accepted Answer

For oxygen in a rigid container, use the diatomic molar heat capacity at constant volume.
$C_{V} = \frac{5 R}{2}$
$C_{V} \frac{d T}{d t} = \frac{K A}{d} (2 T_{0} - T)$
$\frac{d ( 2 T _{0} - T )}{2 T _{0} - T} = - \frac{2 K A}{5 d R} d t$
$2 T_{0} - T = T_{0} e^{- 2 K A t / (5 d R)}$
$T = T_{0} (2 - e^{- 2 K A t / (5 d R)})$
Answer A.

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