Calculating Entropy Change in a Heat Engine Operating at Different Temperatures

In summary: ANDA: In summary, the heat engine transfers heat between two reservoirs and achieves a net increase in entropy.
  • #1
will_lansing
19
0

Homework Statement


A heat engine operates between a high-temperature reservoir at 690 K and a low-temperature reservoir at 320 K. In one cycle, the engine absorbs 6700 J of heat from the high-temperature reservoir and does 2200 J of work. What is the magnitude of the net change in entropy as a result of this cycle?



Homework Equations



delta S =Q/T

The Attempt at a Solution


Qh= 6700
Th=690
Qc=Qh-W=6700-2200=4500
Tc=320

delta S= (-6700/690)+(4500/320)= 4.4 J/K

But i got the answer wrong, Where did i make a mistake, did i not round off correctly, or is the formula i used incorrect.
 
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  • #2
will_lansing said:

Homework Statement


A heat engine operates between a high-temperature reservoir at 690 K and a low-temperature reservoir at 320 K. In one cycle, the engine absorbs 6700 J of heat from the high-temperature reservoir and does 2200 J of work. What is the magnitude of the net change in entropy as a result of this cycle?



Homework Equations



delta S =Q/T

The Attempt at a Solution


Qh= 6700
Th=690
Qc=Qh-W=6700-2200=4500
I believe I see a sign error there. Start over from the equation for the First Law and be careful with the signs.
 
  • #3
I still don't see where i went wrong. can you please explain a bit more.
 
  • #4
will_lansing said:

Homework Statement


A heat engine operates between a high-temperature reservoir at 690 K and a low-temperature reservoir at 320 K. In one cycle, the engine absorbs 6700 J of heat from the high-temperature reservoir and does 2200 J of work. What is the magnitude of the net change in entropy as a result of this cycle?



Homework Equations



delta S =Q/T

The Attempt at a Solution


Qh= 6700
Th=690
Qc=Qh-W=6700-2200=4500
Tc=320

delta S= (-6700/690)+(4500/320)= 4.4 J/K

But i got the answer wrong, Where did i make a mistake, did i not round off correctly, or is the formula i used incorrect.

Your method is correct. And you are correct to use two significant figures. It is just a problem with when to round off your figures. I think they want you to calculate each of the entropy changes of the hot reservoir and cold reservoir separately to two significant figures and then take the total.

The change in entropy of the engine is 0 since it returns to its initial state in one complete cycle. In one cycle, the hot reservoir has lost 6700 joules and the cold reservoir has gained 4500 joules. So the total entropy change is that of the reservoirs only, which is:

[tex]\Delta S = -\Delta Q_h/T_h + \Delta Q_c/T_c = -6700/690 + 4500/320 = -9.7 + 14 = 4.3 J/K[/tex]

AM
 

1. What is a heat engine?

A heat engine is a device that converts heat energy into mechanical work. It typically involves the transfer of heat from a high temperature source to a lower temperature sink, resulting in the production of useful work.

2. What is entropy in relation to heat engines?

Entropy is a measure of the disorder or randomness in a system. In the context of heat engines, it is a measure of how much energy cannot be converted into work due to the irreversible processes that occur during the engine's operation.

3. How does entropy affect the efficiency of a heat engine?

Entropy has a direct impact on the efficiency of a heat engine. The second law of thermodynamics states that the total entropy of a closed system always increases over time. This means that as the engine operates, some of the energy is lost as heat, reducing its efficiency.

4. Can entropy be reversed in a heat engine?

No, entropy cannot be reversed in a heat engine. As mentioned earlier, the second law of thermodynamics states that the total entropy of a closed system can never decrease. Therefore, once entropy is generated in a heat engine, it cannot be reversed.

5. How can entropy be minimized in a heat engine?

Entropy can be minimized in a heat engine by reducing the amount of energy lost as heat. This can be achieved by improving the design and materials used in the engine, as well as implementing efficient heat transfer methods. Additionally, regular maintenance and proper operation can also help minimize entropy in a heat engine.

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