Question

A compressor with a compression ratio of 8 takes in air at an atmospheric pressure of 100 x `10^3` N/`m^2` and a temperature of 17°C. If the pressure after compression is 900 x `10^3` N/`m^2` calculate the final temperature of the air.?

A compressor with a compression ratio of 8 takes in air at an atmospheric pressure of 100 x `10^3` N/`m^2` and a temperature of 17°C. If the pressure after compression is 900 x `10^3` N/`m^2` calculate the final temperature of the air.?

Answer 1

The final temperature is `=270.3^@C`

Explanation:

Apply the equation

`T_2/T_1=(p_2/p_1)^((gamma-1)/gamma)`

The initial temperature is `T_1=17+273=290K`

The initial pressure is `p_1=10^5Pa`

The final pressure is `p_2=9*10^5Pa`

As `1Nm^-2=1Pa`

The adiabatic index for air `gamma=1.4`

Therefore,

`T_2=(p_2/p_1)^((gamma-1)/gamma)*T_1`

`=((9*10^5)/(10^5))^(0.4/1.4)*290`

`=543.3K`

`=(543.3-273)*""^@C`

`=270.3^@C`