Question

A 2.5 mol sample of ideal gas initially at 1 atm and 25 °C is expanded isothermally (ΔT = 0) and reversibly to twice its original volume.

What is the change in internal energy?

Answer 1

For isothermal expansion

Change in internal energy(∆U) =0

For isothermal process

Work done(w) = - nRTln(2V1/V1)

   = -( 2.5 mole × 8.314(J/mol K ) × 298.15K × ln(2)

= - ( 2.5mole × 8.314(J/mol K ) × 298.15K ×2.303log(2)

   = - 4296.2J

According to first law of thermodynamics

   ∆U = q + w

∆U =0

q + w = 0

   q = -w

   q = - ( -4296.2J)

   = + 4296.2J

So , 4296.2J of heat is added to the system and all the added heat converted to work