Question

Gas at a pressure of 0.85 bar, volume 0.25m^3 and temperature 18°C, is compressed until the pressure is 2.8 bar and volume is 0.115m^3, Calculate the compression index and the final temperature.

Answer 1

n=1.53

T₂ = 166.16 °C

Step-by-step explanation:

Given that

P₁=0.85 bar

V₁= 0.25 m³

P₂=2.8 bar

V₂=0.115 m³

Lets take compression index is n

So

`PV^n=C`

`P_1V^n_1=P_2V^n_2`

Now by putting the values

`(P_1)/(P_2)=\left((V_2)/(V_1)\right)^n`

`P_1V^n_1=P_2V^n_2`

`0.85* 0.25^n=2.8* 0.115^n`

`(2.8)/(0.85)=\left((0.25)/(0.115)\right)^n`

`3.29=2.17^n`

ln 3.29 = n ln 2.17

n=1.53

T₁=18°C=273+ 18 = 291 K

Lets final temperature =T₂

`T_1V_1^(n-1)=T_2V_2^(n-1)`

`291* 0.25^(1.53-1)=T_2* 0.115^(1.53-1)`

T₂=439.16 K

T₂ = 166.16 °C