Question

A closed, cylindrical piston contains an ideal gas initially at a volume of 1.00L, temperature of 25.0ºC and internal pressure of 1.00 bar. The gas is compressed by applying an external pressure of 1.5bar to a volume of 0.200L.

a. (20 pts) What is the work done in compressing the gas?

b. (15 pts) If the above piston had diathermal walls and the process occurred isothermally, how much heat would be exchanged?

Show steps and Ill rate! Thanks for the help.

Answer 1

1) For isothermal compression,   

W = 1mol * 8.31451 x 10^-2 L.bar/ mol.K * 25⁰C * ln (0.2/1.0)L

= 1mol * 8.31451 x 10^-2 L.bar/ mol.K * 298K * ln (0.2/1.0)

= 24.78 L.bar * (-1.61)

= 40 L.bar

W = 4000 J = 4 kJ

2) For ideal gases, at constant temperature, the internal energy of the system is constant, and so ΔU = 0.

According to First Law of Thermodynamics:

ΔU = Q + W

Q = −W for the isothermal compression or expansion of ideal gases. (ΔU = 0)

Q = -4 kJ