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One mole of nitrogen gas confined within a cylinder by a
Chapter 5, Problem 81P(choose chapter or problem)
One mole of nitrogen gas confined within a cylinder by a piston is heated from 0°C to 819°C at 1.00 atm.
(a) Calculate the work of expansion of the gas in joules (\(1 J = 9.87 \times 10^{-3} \mathrm{~atm} \cdot \mathrm{L}\)). Assume all the energy is used to do work.
(b) What would be the temperature change if the gas were heated with the same amount of energy in a container of fixed volume? (Assume the specific heat capacity of \(\mathrm{N}_{2}\) is \(1.00 \mathrm{~J} / \mathrm{g} \cdot \mathrm{K}\).)
Questions & Answers
QUESTION:
One mole of nitrogen gas confined within a cylinder by a piston is heated from 0°C to 819°C at 1.00 atm.
(a) Calculate the work of expansion of the gas in joules (\(1 J = 9.87 \times 10^{-3} \mathrm{~atm} \cdot \mathrm{L}\)). Assume all the energy is used to do work.
(b) What would be the temperature change if the gas were heated with the same amount of energy in a container of fixed volume? (Assume the specific heat capacity of \(\mathrm{N}_{2}\) is \(1.00 \mathrm{~J} / \mathrm{g} \cdot \mathrm{K}\).)
ANSWER:
Step 1 of 3
(a) Here we have to calculate the work of expansion of the gas in joules (\(1 \mathrm{~J}=9.87 \times 10^{-3} \mathrm{atm·L}\)).
Given:
In this question it has been given that one mole of nitrogen gas confined within a cylinder by a piston is heated from 0°C to 819°C at 1.00 atm.
Change in temperature T= (819-0) oC = 819oC = 819 K
n (mole) = 1 mole \(\mathrm{N}_{2}\) gas
The work done due to expansion can be calculated as,
\(\mathrm{W}=\mathrm{P} \Delta V\)--------(1)
Where P is the pressure and \(\Delta V\) is the change in volume.
According to ideal gas equation it is known that,
\(\mathrm{P} \Delta V=\mathrm{nR} \Delta T\)----------(2)