How Does Compressing an Ideal Gas Affect Its Temperature?

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Homework Help Overview

The problem involves an ideal gas contained in a cylinder with a movable piston, initially at a specific temperature, pressure, and volume. The scenario describes the gas being compressed to a smaller volume and a higher pressure, prompting a question about the resulting temperature change.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to apply the ideal gas law in a ratio form to find the final temperature after compression. Some participants question the use of temperature units, suggesting that absolute temperatures must be used in the calculations.

Discussion Status

Participants are actively engaging with the problem, with some providing clarifications about the necessity of using absolute temperature in the calculations. There is an acknowledgment of a misunderstanding regarding the use of temperature units in the context of ratios versus differences.

Contextual Notes

The original poster's calculations appear to be based on an incorrect assumption about temperature units, which has been pointed out by other participants. The discussion reflects a focus on ensuring the correct application of principles related to temperature in gas laws.

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Homework Statement



A cylinder fitted with a movable piston contains ideal gas at 27C, pressure .5 x 10^5 Pa, and volume 1.25 m^3. What will be the final temperature if the gas is compressed to .8 m^3 and the pressure rises to .82 x 10^5 Pa.

A) 125 C
B) 154 C
C) 246 C
D) 67.7 C
E) 41.8 C

Homework Equations



P1V1/T1=P2V2/T2

The Attempt at a Solution



I thought this problem was going to be pretty simple. (.5 x 10^5 Pa x 1.25 m^3)/27 = (.82 x 10^5 Pa x .8 m^3)/T2. I keep getting T2 is equal to 28.3392. Is there something I'm missing? It seems like the pressure/volume ratio doesn't change that drastically so the temperatures would be close but the closest answer is at ~15 C increase. Any help is appreciated.
 
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You have to use absolute temperatures.

Chet
 
Chestermiller said:
You have to use absolute temperatures.

Chet

Got it. I thought since it was ratios the units wouldn't affect the final outcome but I was wrong.
 
Only when you're talking about temperature DIFFERENCES - not ratios - you may replace Kelvins with Celsius.
 

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