Efficiency and Temperature in Heat Engine Cycles: Approaching Parts B, C, and D

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  • #1
singularcell
1
0
Homework Statement
Need help with b,c,d.
Relevant Equations
Wnet/QH
e-carnot = 1-(Tc/Th)
Screenshot 2023-05-17 204522.png
SmartSelect_20230517_204248_Samsung Notes (1).jpg

I didn't have much trouble with part a but I'm struggling with b,c, and d. I considered the efficiency formula for a heat engine e = work done by engine/ qh
but i am unsure of how to approach it.
for part c) not sure how i can get to Tc without knowing Th
for d) my gut is telling me 5/2 but i have no explanation for that. Any guidance/help is appreciated
 
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  • #2
Let's see what you've done so far in part (b).
 

FAQ: Efficiency and Temperature in Heat Engine Cycles: Approaching Parts B, C, and D

What is the relationship between efficiency and temperature in heat engine cycles?

The efficiency of a heat engine cycle is strongly dependent on the temperature difference between the heat source and the heat sink. According to the second law of thermodynamics, the maximum possible efficiency of a heat engine operating between two reservoirs is given by the Carnot efficiency, which is 1 - (T_c/T_h), where T_c is the temperature of the cold reservoir and T_h is the temperature of the hot reservoir. As the temperature difference increases, the efficiency of the heat engine also increases.

How does the Carnot cycle represent the ideal efficiency of heat engines?

The Carnot cycle represents the theoretical maximum efficiency that any heat engine can achieve when operating between two temperature reservoirs. It consists of two isothermal processes (heat addition and heat rejection) and two adiabatic processes (expansion and compression). The efficiency of a Carnot engine is given by 1 - (T_c/T_h), making it the benchmark for comparing the performance of real heat engines.

What factors limit the efficiency of real heat engines compared to the Carnot cycle?

Real heat engines are limited by several factors that prevent them from achieving Carnot efficiency. These include irreversibilities such as friction, non-ideal gas behavior, heat losses, and finite-time processes. Additionally, practical considerations like material limitations and mechanical imperfections further reduce the efficiency compared to the ideal Carnot cycle.

How does increasing the temperature of the heat source affect the efficiency of a heat engine?

Increasing the temperature of the heat source (T_h) generally increases the efficiency of a heat engine. According to the Carnot efficiency formula, as T_h increases while T_c remains constant, the term (T_c/T_h) becomes smaller, thus increasing the overall efficiency. However, practical limitations such as material strength and thermal stresses must be considered when raising the temperature of the heat source.

What are the practical implications of the second law of thermodynamics for heat engine design?

The second law of thermodynamics implies that no heat engine can be 100% efficient because some energy will always be lost as waste heat to the cold reservoir. This understanding drives the design of heat engines to maximize efficiency by optimizing the temperature difference between the heat source and sink, minimizing irreversibilities, and improving component materials and engineering. It also encourages the development of combined cycles and waste heat recovery systems to enhance overall energy utilization.

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