Question

0.078 kg of a carbon monoxide initially exists at 130 kPa and 120oC. The gas is then expanded polytropically to a state of 100 kPa and 100oC. Sketch the P-V diagram for this process. Also determine the value of n (index) and the boundary work done during this process.

Answer 1

Mass of carbon monoxide= 0.078 kg, Initial pressure P₁= 130 kPa, T₁=120⁰C=120+273=393 K and following polytropic process and P₂=100 kPa and T₂=100⁰C+273=373 K

$\frac{T_2}{T_1}=\frac{P_2}{P_1}^{\frac{n-1}{n}}$

$\frac{373}{393}=\frac{100}{130}^{\frac{n-1}{n}}$

$0.949=0.769^{\frac{n-1}{n}}$

On taking log both sides

log(0.949)= $\frac{n-1}{n}log(0.769)$

-0.0227= $\frac{n-1}{n}$ (-0.114)

0.0227n=0.114n-0.114

0.0913 n= 0.114

n= 1.248

Now, here using relation for polytropic process we can find value of V1 and V2 as value of mass of as is given so we get the following graph