4.6 Isothermal Expansion of Nitrogen

Problem Statement:

A cylinder with a movable piston contains 1 kg of nitrogen at 100 kPa and 300 K. It undergoes an isothermal expansion until the volume triples. Calculate the boundary work done during this process and the heat transfer involved.

Solution:

import CoolProp.CoolProp as CP
import math

# Given values
m = 1.0  # Mass of nitrogen in kg
T = 300  # Temperature in Kelvin (constant)
P1 = 100000  # Initial pressure in Pa
V1 = m * CP.PropsSI('Dmolar', 'T', T, 'P', P1, 'Nitrogen')  # Initial volume using density
V2 = 3 * V1  # Final volume (tripled)

# 1. Boundary work (W)
# For isothermal process, W = nRT ln(V2/V1)
R = CP.PropsSI('GAS_CONSTANT', 'Nitrogen') / CP.PropsSI('MOLAR_MASS', 'Nitrogen')
W = m * R * T * math.log(V2 / V1)

# 2. Heat transfer (Q)
# For an isothermal process, Q = W
Q = W

# Output the results
print(f"Boundary work done (W): {round(W/1e3,1)} kJ")
print(f"Heat transfer (Q): {round(Q/1e3,1)} kJ")

Boundary work done (W): 97.8 kJ
Heat transfer (Q): 97.8 kJ