Exploring Work Output of a Carnot Cycle

In summary, the Carnot cycle involves a reversible isothermal expansion of a gas at a high temperature, during which the gas absorbs heat and performs work on the surroundings. This work is not counted towards the total work output of the cycle, as it is equal to the heat transferred. This also applies to a boiler in a Carnot cycle, which does not have a piston and therefore does not do any work, but still facilitates the isothermal heat transfer.
  • #1
Red_CCF
532
0
Hi

From http://en.wikipedia.org/wiki/Carnot_cycle

"Reversible isothermal expansion of the gas at the "hot" temperature, TH (isothermal heat addition). During this step the expanding gas makes the piston work on the surroundings. The gas expansion is propelled by absorption of quantity Q1 of heat from the high temperature reservoir."

I was wondering why the work done on the surroundings at this stage does not count toward the total work output of the cycle and why it is not used?

Thanks
 
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  • #2
It does.

In fact, from the first law of thermodynamics, you can make Heat = Work + Delta U, though as it is a cycle and U is a state variable, Delta U in the cycle is null, so the heat transferred is equal to work.
 
  • #3
Hobold said:
It does.

In fact, from the first law of thermodynamics, you can make Heat = Work + Delta U, though as it is a cycle and U is a state variable, Delta U in the cycle is null, so the heat transferred is equal to work.

Hi, thanks for the response

What about for a boiler? A boiler in a heat engine operating a Carnot cycle does not have a piston (it is rigid), in this case, although it is also responsible for Process 1-2 in a Carnot cycle it does no work right? Also, how does a rigid boiler maintain isothermal heat transfer?

Thanks
 
  • #4
does the steam from the boiler go anywhere and do anything?
 

1. What is a Carnot Cycle?

A Carnot Cycle is a theoretical thermodynamic cycle that describes the most efficient way to convert heat energy into work. It consists of four reversible processes: isothermal expansion, adiabatic expansion, isothermal compression, and adiabatic compression.

2. How does a Carnot Cycle work?

In a Carnot Cycle, a working fluid (such as a gas) is contained in a closed system and undergoes a series of thermodynamic processes. Heat is added to the system during the isothermal expansion process, causing the gas to expand and do work. The gas then undergoes adiabatic expansion, where it cools down and loses heat. Next, the gas is compressed isothermally, releasing more heat. Finally, the gas is compressed adiabatically to its original state, completing the cycle.

3. What is the efficiency of a Carnot Cycle?

The efficiency of a Carnot Cycle is given by the formula: efficiency = (Th-Tc)/Th, where Th is the temperature of the heat source and Tc is the temperature of the heat sink. This means that the efficiency is determined by the temperature difference between the two reservoirs, and it is always less than 1. In other words, a Carnot Cycle is the most efficient possible heat engine.

4. What factors affect the work output of a Carnot Cycle?

The work output of a Carnot Cycle is affected by several factors, including the temperature of the heat source and sink, the type of working fluid, and the pressure and volume of the system. The efficiency of the cycle also plays a role in determining the work output.

5. How is the work output of a Carnot Cycle calculated?

The work output of a Carnot Cycle can be calculated using the formula: work output = Qh(1-Tc/Th), where Qh is the heat added to the system during the isothermal expansion process and Tc and Th are the temperatures of the heat sink and source, respectively. This formula takes into account the efficiency of the cycle and the temperature difference between the two reservoirs.

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