Thermodynamics: Carnot Engine, WHY IS Qhot NEGATIVE?

[Minari]

Homework Statement

1. A heat engine operating between 200°C and 80.0°C achieves 20.0% of the maximum possible efficiency. What energy input will enable the engine to perform 10.0 kJ of work?

Homework Equations

e =1- Tc/Th
W=e*Qh

The Attempt at a Solution

I got the answer but I don't understand why Qh is negative and could you also explain why work is negative too? I'm guessing since the work is the output its negative? But why would the Qh be negative to isn't it the input? Also could you tell/explain when W, Qh and Qc are positive and negative? Thank you.

 

[Rick88]

From U=Q+W

U + -> Internal energy gained by system
U - -> Internal energy lost by system

Q + -> Heat entering the system
Q - -> Heat leaving the system

W + -> Work done on the system
W - -> Work done by the systemR.

 

[Andrew Mason]

Homework Statement

1. A heat engine operating between 200°C and 80.0°C achieves 20.0% of the maximum possible efficiency. What energy input will enable the engine to perform 10.0 kJ of work?

Homework Equations

e =1- Tc/Th
W=e*Qh

The Attempt at a Solution

I got the answer but I don't understand why Qh is negative and could you also explain why work is negative too? I'm guessing since the work is the output its negative? But why would the Qh be negative to isn't it the input? Also could you tell/explain when W, Qh and Qc are positive and negative? Thank you.

As Rick88 points out, it is the convention to denote heat leaving (eg. a reservoir) as negative and heat entering as positive. Whether Qh is negative or positive depends on your reference point. To the gas in the heat engine,
Qh is positive and Qc is negative. The convention for Work is less universal. The first law is now commonly written (in differential form):

dQ = dU + dW

where dW is the work done BY the system. In this form, work done BY the system is POSITIVE and work done ON the system is NEGATIVE. But it is just a convention. Not long ago, most textbooks used the opposite convention for W.

AM