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Using Energy Concepts and the Ideal Gas ModelA
Chapter 3, Problem 136P(choose chapter or problem)
A piston-cylinder assembly contains carbon monoxide modeled as an ideal gas with constant specific heat ratio, k =1.4. The carbon monoxide undergoes a polytropic expansion with n = k from an initial state, where \(T_1=200^{\circ} \mathrm{F}\) and \(p_1=40 \mathrm{lbf} / \mathrm{in}^2\), to a final state, where the volume is twice the initial volume. Determine (a) the final temperature, in \({ }^{\circ} \mathrm{F}\), and final pressure, in \( \mathrm{lbf} / \mathrm{in.}^2\), and (b) the work and heat transfer, each in \(\mathrm{Btu} / \mathrm{lb}\).
Questions & Answers
QUESTION:
A piston-cylinder assembly contains carbon monoxide modeled as an ideal gas with constant specific heat ratio, k =1.4. The carbon monoxide undergoes a polytropic expansion with n = k from an initial state, where \(T_1=200^{\circ} \mathrm{F}\) and \(p_1=40 \mathrm{lbf} / \mathrm{in}^2\), to a final state, where the volume is twice the initial volume. Determine (a) the final temperature, in \({ }^{\circ} \mathrm{F}\), and final pressure, in \( \mathrm{lbf} / \mathrm{in.}^2\), and (b) the work and heat transfer, each in \(\mathrm{Btu} / \mathrm{lb}\).
ANSWER:a)
Step 1 of 4
We have to find the final temperature and pressure of carbon monoxide which undergoes a polytropic expansion withfrom an initial state, where
= 200°F and
= 40 lbf/in.2, to a final state.
The final temperature can be found using the equation for the ideal gas
(
Given data :
,
and
oF
Thus,
(
= (
=
=
oF