2. Consider an insulated cylinder with a movable insulated piston (see figure be
ID: 1587147 • Letter: 2
Question
2. Consider an insulated cylinder with a movable insulated piston (see figure below). Initially the cylinder contains an ideal gas at temperature T1 and pressure Pi on both sides of the piston, which is located in the middle of the cylinder. Now add heat to gas on the left side of the piston onlv, which causes it to expand, moving the piston and compressing the gas on the right side of the piston. Enough heat is added so that the gas on the right decreases its volume by a factor of t wo. a. What is the final temperature of the gas on the right side of the piston? (5 pts) b. What is the final temperature on the left side? (5 pts) c. What is the minimum amount of heat needed to reach the final state? (15 pts) (You may assume the constant-volume heat capacity is Cv and independent of temperature.)Explanation / Answer
I think you need to use ideal gas relationship
a)
on right side, there is no heat being added. So final temperature will be same as initial temperature
Answer: T1
b)
Pressure on right side be P2
V2 = V1/2
use on right side:
P1*V1 = P2*V2
P1*V1 = P2*V1/2
P2 = 2*P1
This will be pressure on left side as well
on left side,
V2= V1+V1/2=3*V1/2
P2=2*P1
T2=?
use:
P2*V2/T2 = P1*V1/T1
2*P1*3*V1/(2*T2) = P1*V1/T1
T2=3*T1
Answer: Temperature will be 3*T1
c)
heat added = CV*(T2-T1)
= CV*(3*T1-T1)
= 2*CV*T1
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