A piston system absorbs 50.5 J of energy in the form of heat from the surroundings. The piston is working against a pressure of 0.491 atm. The final volume of the system is 56.2 L. What was the initial volume of the system if the internal energy of the system decreased by 106.0 J? (To convert between L∙atm and J, use 1 L∙atm = 101.3 J.)

The initial volume of the system: V₁ = 53.06 L

Explanation:

Given: heat absorbed by system: q = 50.5 J, Pressure: P = 0.491 atm, Final volume: V₂ = 56.2 L, The change in the internal energy: ΔE = - 106.0 J

Initial volume: V₁ = ? L

According to the First Law of Thermodynamics:

ΔE = q - PΔV

⇒ PΔV = q - ΔE = 50.5 J - (-106.0 J) = 156.5 J

As, 1 L∙atm = 101.3 J ⇒ 1 J = (1 : 101.3) L∙atm

⇒ PΔV = 156.5 J = (156.5 : 101.3) L∙atm = 1.54 L∙atm

So,

ΔV = 1.54 L∙atm : P = 1.54 L∙atm : 0.491 atm = 3.14 L

∵ ΔV = V₂ - V₁ = 3.14 L

⇒ V₁ = V₂ - 3.14 L = 56.2 L - 3.14 L = 53.06 L

Therefore, the initial volume of the system: V₁ = 53.06 L