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 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.

Answer 1

Data: P = 1 atm = 1.013 x 10⁵ Pa, V₁ =5 litres =5 x 10^-3 m³,

V₂ = 10 Litres = 10 x 10^-3 m³, Q = 400J.

The work done by the system (gas in this case) 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 10²J

The change in the internal energy of the system,

ΔU = Q − W = 400 − 506.5 = −106.5J

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