Question

Which of the two gases, air or carbon dioxide, has the lower final temperature as it is expanded isentropically from 800 kPa and 400°C to 100 kPa in a piston-cylinder device. Use room temperature specific heats.

Answer 1

Carbon dioxide have higher temperature at the final stage.

Step-by-step explanation:

Given that

`P_1=800 KPa,T_1=400 C,P_2=100 KPa`

We know that

γ=1.28 for carbon dioxide

γ=1.4 for air

For isentropic expansion

`(T_2)/(T_1)=\left((P_2)/(P_1)\right)^{(\gamma -1)/(\gamma)}`

Now for carbon dioxide γ=1.28

`(T_2)/(673)=\left((100)/(800)\right)^{(1.28 -1)/(1.28)}`

`T_2=427.03 K`

Now for air γ=1.4

`(T_2)/(673)=\left((100)/(800)\right)^{(1.4 -1)/(1.4)}`

`T_2=372.07 K`

So carbon dioxide have higher temperature at the final stage.