Question

My Notes A container is divided into two equal compartments by a partition. One compartment is initially filled with helium at a temperature of 240 K; the other is filled with nitrogen at a temperature of 315 K. Both gases are at the same pressure. If we remove the partition and allow the gases to mix, what will be their final temperature?

Answer 1

Answer:

$final-temperature = T_{f} = 252.51K$

Explanation:

we can solve this problem by using the first law of thermodynamics.

    $\Delta U= Q-W$

Q= heat added

U= internal energy

W= work done by system

                        $E_{final}= E_{initial}$

$C_{v} (N_{2}) C_{v}(He) T_{f} =C_{v}( N_{2}) T_{N_{2} } C_{v} (He) T_{He}$    (1)

$C_{v}(N_{2})=1.04\frac{KJ}{Kg K}$

$C_{v}(He)=5.193\frac{KJ}{Kg K}$

now

From equation 1

$T_{f}=\frac{C_{v}( N_{2}) T_{N_{2} } C_{v} (He) T_{He}}{C_{v} (N_{2}) C_{v}(He)}$

$T_{f} = \frac{315\times1.04+5.193\times240}{1.04+5.193}$

$T_{f} = 252.51K$