Question

In a reversible compression process, 1 mol of ideal gas in a piston cylinder device
undergoes a pressure change from 1 bar to pressure ‘P’ and temperature increases
from 400 K to 900 K. The compression path is described by PV1.3 = constant.
Calculate the final pressure and heat transferred.
[Given - Heat capacity of gas (Cp) = 30.84 J/mol-K]

Answer 1

The given relation between pressure volume is given below:

…… (1)

Write the ideal gas equation as follows:

…… (2)

Here,  is the pressure , is the volume,  is the temperature,  is the universal gas constant and  is the number of moles.

In equation (2),  is constant and  is one mole then rearrange equation (2) as follows:

…… (3)

Answer 2

Answer:

The final pressure is 2.25 bar. The heat transferred is 15.420 KJ.

Explanation:

Given:
Number of moles(n)=1

Pressure 1(P₁)=1 bar

Pressure 2(P₂)=P

Temperature 1(T₁)=400K

Temperature 2(T₂)=900K

To find: P₂=? Heat transferred(Q)=?
Solution:
For an ideal gas,

PV=nRT

∴$\frac{P_{1} }{P_{2} } =\frac{T_{1} }{T_{2} }$

∴1/P=400/900

∴900/400=P

∴P=2.25 bar

The final pressure is 2.25 bar.

We know that,

$Q=nCp$ΔT

=1*30.84*500

=15420J

=15.420 KJ

The heat transferred is 15.420 KJ.