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

`final-temperature = T_(f) = 252.51K`

Step-by-step 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(KJ)/(Kg K)`

`C_(v)(He)=5.193(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) = (315*1.04+5.193*240)/(1.04+5.193)`

`T_(f) = 252.51K`