Isothermal Compressor Work
Isothermal Compressor Work
Compressing a gas slowly (isothermally) takes work set by the pressure ratio — the ideal minimum for a gas compressor.
The work is W = p_1·V_1·ln(p_2/p_1). where p_1, V_1 are the initial pressure and volume and p_2 the final pressure.
Inputs
p_1 := 100 kPa=100000 Pa
V_1 := 0.5 m^3=0.5 m^3
p_2 := 700 kPa=700000 Pa
Apply the isothermal compression work.
W := p_1·V_1·ln(p_2/p_1)=97295.51 Nm
Results
The logarithm means each further doubling of pressure costs the same work. Real (adiabatic) compression needs more and heats the gas.
Assumptions & limitations
- Ideal gas, isothermal.
- Reversible (quasi-static).
- Closed system.