Question

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 liters to a volume of 10 liters. In doing so it absorbs 400J of thermal energy from its surroundings. Determine the change in the internal energy of the system.

Answer 1

Given:

P = 1 atm = 1.013 x 10⁵ Pa,
V₁ = 5 liters = 5 x 10^-3 m³,
V₂ = 10 liters = 10 x 10^-3 m³,
Q = 400 J

The work done by the system on its surroundings,

W = P(V₂ - V₁)

= (1.013 x 10⁵) (10 x 10^-3 - 5 x 10^-3)

= 1.013 (5 x 10²)

= 5.065 x 10² J

The change in the internal energy of the system,

ΔU = Q - W = 400 - 506.5 = -106.5 J

The negative sign shows that there is a decrease in the internal energy of the system.