Question

1. 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? (101.3 j = 1 l atm)

Explanation:

Step1: Convert work from joules to L·atm

Given \(101.3\ J = 1\ L\cdot atm\), so \(w=- 288\ J\).
\(w=-288\ J\times\frac{1\ L\cdot atm}{101.3\ J}\approx - 2.843\ L\cdot atm\) (work done on surroundings, so \(w\) is negative)

Step2: Use the formula \(w=-P\Delta V=-P(V_{f}-V_{i})\)

We know \(P = 2.00\ atm\), \(V_{i}=0.250\ L\), and \(w=-2.843\ L\cdot atm\)
Substitute into the formula: \(-2.843\ L\cdot atm=-2.00\ atm\times(V_{f}- 0.250\ L)\)

Step3: Solve for \(V_{f}\)

First, divide both sides by \(-2.00\ atm\):
\(\frac{-2.843\ L\cdot atm}{-2.00\ atm}=V_{f}-0.250\ L\)
\(1.4215\ L=V_{f}-0.250\ L\)
Then add \(0.250\ L\) to both sides:
\(V_{f}=1.4215\ L + 0.250\ L=1.67\ L\)

Answer:

\(1.67\ L\)