Carnot Cycle: Analysis of Energy Exchange

[physics123]

A refrigerator operates on a Carnot cycle. In this cycles, it absorbs 120 J of energy at a temperature Tc while 300 J of work is done on the gas undergoing the cycle.

How much energy is exhausted as heat during this process?

The answer is 420 J.

I am unsure of where to start for this question as we are not given temperatures.

 

[zenmaster99]

Recall that, in any cyclic process, the gas must return to its original state. So, in one cycle,

$$\Delta U=Q-W=0$$

Therefore, work done (300 J) must equal heat expelled. And any heat added (120 J) must also be expelled.

 

[physics123]

Recall that, in any cyclic process, the gas must return to its original state. So, in one cycle,

$$\Delta U=Q-W=0$$

Therefore, work done (300 J) must equal heat expelled. And any heat added (120 J) must also be expelled.

so to find energy exhausted as heat, it is as simple as adding the work plus any heat added?

 

[physics123]

so to find energy exhausted as heat, it is as simple as adding the work plus any heat added?

Could you then explain this question?
A heat engine operates on a Carnot cycle. In this cycles, it absorbs 420J of energy while it expands in contact with a reservoir of temperature Th. The heat engine does a net 300J during the full cycle.

The answer is 120J, so why isn't the energy added? What is the difference between absorbing energy at Th and Tc?

 

[zenmaster99]

In this case, the engine takes in 420 J from the hot reservoir. This must be expelled as either heat or work. 300 J is returned as work, therefore 120 J must be heat.

Hang on, let me look for the diagram I'm thinking of...

Here it is: https://en.wikipedia.org/wiki/Heat_engine#/media/File:Heat_engine.png

Notice that what goes in must come out as either work or heat. Although this diagram tries to be all-encompassing by including a little loss mechanism, you needn't worry about that at this level.