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A sample of nitrogen gas expands in volume from 1.6 L to
Chapter 6, Problem 15P(choose chapter or problem)
A sample of nitrogen gas expands in volume from \(1.6 \mathrm{~L}\) to \(5.4 \mathrm{~L}\) at constant temperature. Calculate the work done in joules if the gas expands (a) against a vacuum, (b) against a constant pressure of \(0.80 \mathrm{~atm}\), and (c) against a constant pressure of \(3.7 \mathrm{~atm}\).
Questions & Answers
QUESTION:
A sample of nitrogen gas expands in volume from \(1.6 \mathrm{~L}\) to \(5.4 \mathrm{~L}\) at constant temperature. Calculate the work done in joules if the gas expands (a) against a vacuum, (b) against a constant pressure of \(0.80 \mathrm{~atm}\), and (c) against a constant pressure of \(3.7 \mathrm{~atm}\).
ANSWER:Step 1 of 3
The goal of the problem is to calculate the work done in joules when the gas expands for given conditions.
Given:
\(\mathrm{V}_{\text {initial }}=1.6 \mathrm{~L}\)
\(\mathrm{~V}_{\text {final }}=5.4 \mathrm{~L}\)
Recall that the work in gas expansion is equal to the product of the external, opposing pressure and the change in volume
(a) Given: against a vacuum:
The work done is calculated using the formula:
\(\mathrm{w}=-\mathrm{P} \Delta \mathrm{V}\) Where \(\mathrm{P}=\) Pressure \(\Delta \mathrm{V}=\) change in volume \(=\mathrm{V}_{\text {final }}-\mathrm{V}_{\text {initial }}\)
Therefore, work done will be:
=-(0)(5.4-1.6) L
= 0
Hence, the work done in joules when the gas expands against a vacuum is \(-3.0 \times 10^{2} \mathrm{~J}\)