Work required to extract heat from a refrigerator

AI Thread Summary
The discussion revolves around the calculation of work required to extract heat from a refrigerator, where the original poster received a negative value contrary to the answer key's positive value of +0.043 cal. The poster's approach involved using the principles of a reversible engine and the relationship between absorbed and rejected heat. Responses highlighted the importance of correctly interpreting the signs of heat transfer and work, emphasizing that if the system does work on the environment, work should be considered positive. Ultimately, the poster acknowledged a misunderstanding in their calculations and expressed gratitude for the clarification. The conversation underscores the significance of adhering to conventional sign conventions in thermodynamic calculations.
guyvsdcsniper
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Homework Statement
A reversible refrigerator engine extracts heat from
the inside of a refrigerator compartment kept at 8°C and rejects unwanted
heat QH to its 20°C exterior. Find the work required to extract one calorie
from the interior of the refrigerator compartment
Relevant Equations
dQ/T=0
The answer key says the work done should be +.043cal. I am getting a negative sign.

I have posted my work in the attached image.
My logic is that since this a reversible engine we can say the integral of dQ/T=0. Looking at the cycle, Qc isi being absorbed (Qc>0) and Qh is being rejected (Qh<0). Then we can say Qc/Tc-Qh/Th=0.

Solving for Qh, we get 1.0427cal.
We also know W= the integral of dQ. So we can say W=Qc-Qh.

Doing so makes me get a negative sign.

I guess from my perspective the negative indicates the system is doing work, hence W<0.

Am I doing something wrong/looking at the situation from a different perspective by getting this negative sign?
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quittingthecult said:
Homework Statement:: A reversible refrigerator engine extracts heat from
the inside of a refrigerator compartment kept at 8°C and rejects unwanted
heat QH to its 20°C exterior. Find the work required to extract one calorie
from the interior of the refrigerator compartment
Relevant Equations:: dQ/T=0

The answer key says the work done should be +.043cal. I am getting a negative sign.

I have posted my work in the attached image.
My logic is that since this a reversible engine we can say the integral of dQ/T=0. Looking at the cycle, Qc isi being absorbed (Qc>0) and Qh is being rejected (Qh<0). Then we can say Qc/Tc-Qh/Th=0.
If ##Q_c>0## and ##Q_h<0##, then ##\frac{Q_C}{T_C}-\frac{Q_H}{T_H}## will be positive. You should either have a plus sign in between or use absolute values.

quittingthecult said:
Solving for Qh, we get 1.0427cal.
We also know W= the integral of dQ. So we can say W=Qc-Qh.
Look at the arrows in your diagram. The energy coming into the system is ##|W|+Q_c##, and the energy going out is ##|Q_h|##. Conservation of energy requires ##|Q_h| = |W| + Q_c##.

quittingthecult said:
Doing so makes me get a negative sign.

I guess from my perspective the negative indicates the system is doing work, hence W<0.
The usual convention is if the system does work on the environment, ##W## is positive. Are you using a different convention or did you make a mistake?
 
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vela said:
If ##Q_c>0## and ##Q_h<0##, then ##\frac{Q_C}{T_C}-\frac{Q_H}{T_H}## will be positive. You should either have a plus sign in between or use absolute values.Look at the arrows in your diagram. The energy coming into the system is ##|W|+Q_c##, and the energy going out is ##|Q_h|##. Conservation of energy requires ##|Q_h| = |W| + Q_c##.The usual convention is if the system does work on the environment, ##W## is positive. Are you using a different convention or did you make a mistake?
Ah your right. I overthought this way too hard. I should have just looked at the arrows.

Thank you, your response has helped me realize the mistake i made.
 
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