A cylinder with a moving piston expands from an initial volume of 0.250 L against an external pressure of 2.00 atm. The expansion does 288 J of work on the surroundings. What is the final volume of the cylinder? (1 LLaTeX: / cdot⋅atm = 101.3 J) Group of answer choices

The final volume of the cylinder is 1.67 L

Explanation:

Step 1: Data given

Initial volume = 0.250 L

external pressure = 2.00 atm

Expansion does 288 J of work on the surroundings

Step 2: Definition of reversible work:

Wrev = - P (V2-V1) = - 288 J

The gas did work, so V2>V1 (volume expands) and the work has a negative sign. (Wrev<0)

V2 = (-Wrev/P) + V1

⇒ with Wrev = reverse work (in J)

⇒ with P = the external pressure (in atm)

⇒ with V1 = the initial volume

We can see that your pressure is in atm and energy in J

To convert from J to L * atm we should use a convenient conversion unit using the universal gas constants:

R = 8.314472 J/mol * K and R = 0.08206 L*atm/K*mol

V2 = - (-288 J * (0.08206 L*atm/K*mol / 8.314 J/mol * K)) / 2.00 atm + 0.250L

V2 = 1.67 L

The final volume of the cylinder is 1.67 L