First slide

Heat given

Question

Two rigid boxes containing different ideal gases are placed on a table. Box A contains one mole of nitrogen at temperature $T_{o}$ , while Box B contains one mole of helium at temperature (7/3) T₀. The boxes are then put into thermal contact with each other and heat flows between them until the gases reach a common final temperature (ignore the heat capacity of boxes). Then, the final temperature of the gases T₁ , in terms of T₀ is

Moderate

A

$T_{f} = \frac{7}{3} T_{0}$
B

$T_{f} = \frac{3}{2} T_{0}$
C

$T_{f} = \frac{5}{2} T_{0}$
D

$T_{f} = \frac{3}{7} T_{0}$

Solution

When two gases are mixed together, then
Heat lost by the helium gas = Heat gained by the nitrogen gas
$n_{B} \times {(c_{v})}_{He} \times (\frac{7}{3} T_{0} - T_{f}) = n_{A} \times {(c_{v})}_{N_{2}} \times (T_{f} - T_{0})$
$B o x A 1 m o l e N_{2} T e m p e r a t u r e = T_{0}$ $B o x B 1 m o l e H e T e m p e r a t u r e = \frac{7}{3} T_{0}$
$\Rightarrow 1 \times \frac{3}{2} R \times (\frac{7}{3} T_{0} - T_{f}) = 1 \times \frac{5}{2} R \times (T_{f} - T_{0})$
By solving, we get
$T_{f} = \frac{3}{2} T_{0}$

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