Question

We have a piston (V = 2000cm^3 ) filled with 0.9kg of Oxygen (molar mass of 16g/mol) that is 40 percent efficient. If the Oxygen is at a temperature of 300K and expands isothermally to a volume of 4500cm^3 , how much heat must have been added? How much heat was lost to the environment?

Answer 1

Initial volume, V_i = 2000 cm³

Final volume, V_f = 4500 cm³

Mass of oxygen, m = 0.9 kg

Molar mass, M = 16 g =0.016 kg

Temperature of the gas, T = 300 K

Efficiency, η = 40 %

Number of moles of gas, n = m/M = 0.9/0.016 = 56.25

Work done to expand the gas isothermally, W = 2.303 nRT log(V_f / V_i )

W = 2.303 x 56.25 x 8.31 x 300 x log(4500 /2000 ) = 113738.2 J

Since the efficiency is 40%, work done is 40 % of total heat E added.

Work, W = 40 % of E = 0.4 E

Heat added, E = W/0.4 = 113738.2/0.4 = 284345.5 J

Heat added, E = 284345.5 J

Heat lost to the surrounding = E -W = 284345.5 - 113738.2 = 170607.3 J

Heat lost to the surrounding = 170607.3 J