Question

Solve the following:

a) Calculate ΔU for the irreversible isothermal compression of 1 mole of ideal gas at 290 K from an initial pressure of 3.2 KPa to a final pressure of 46 kPa by an constant external pressure of 46 kPa. Give your answer in kilojoules.

b) Consider a reversible isothermal expansion (or compression) of 4.0 mole(s) of an ideal gas at 28°C from 6.5 atm to 3.0 atm. Calculate the amount of heat transferred to the system in kJ.

Answer 1

a)

For an ideal gas, the internal energy is a function of temperature only so kJ

Reason : As it is said , it is an Isothermal process , which means Temperature is constant so the change in internal energy is Zero

b) Taking expansion

Work done in an isothermal process is given by

W = - 2.303 nRT log (P1/P2)

here n = no. of moles = 4

R = gas constant = 8.314 J/ mo K

T = = 28+273.15 = 301.15 K

P1 = 6.5 atm = 6.5e5 pascal

P2 = 3 atm = 3e5 pascal

W = -2.303 *4 * 8.314 * 301.15 * log (6.5/3)

W = -7744.9263 J = -7.7449 kJ

From 1st law of thermodynamics

here as it is an Isothermal process

So

depending on what expansion or compression sign will apply

here it is expansion so Heat is lost by the system , so -ve

if compression then +ve