Solved Example Problem: First Law of Thermodynamics

A gas contained in a cylinder fitted with a frictionless piston expands against a constant external pressure of 1 atm from a volume of 5 litres to a volume of 10 litres. In doing so it absorbs 400 J of thermal energy from its surroundings. Determine the change in internal energy of system.

Solution:

Given data

q = 400 J

V₁=5L

V₂ = 10L

∆u = q-w (heat is given to the system (+q); work is done by the system(-w) 

∆u    q - PdV

            = 400 J - 1 atm (10-5)L

            =400 J - 5 atm L

[∴ 1 L atm = 101.33 J]

=400 J - 5 × 101.33 J

=400 J - 506.65 J

=- 106.65 J