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

Answer:

n=1.53

T₂ = 166.16 °C

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

$\dfrac{P_1}{P_2}=\left(\dfrac{V_2}{V_1}\right)^n$

$P_1V^n_1=P_2V^n_2$

$0.85\times 0.25^n=2.8\times 0.115^n$

$\dfrac{2.8}{0.85}=\left(\dfrac{0.25}{0.115}\right)^n$

$3.29=2.17^n$

ln 3.29 = n ln 2.17

n=1.53

T₁=18°C=273+ 18 = 291 K

Lets final temperature =T₂

$T_1V_1^{n-1}=T_2V_2^{n-1}$

$291\times 0.25^{1.53-1}=T_2\times 0.115^{1.53-1}$

T₂=439.16 K

T₂ = 166.16 °C