Carnot Cycle: Isothermal Expansion Phase - Work Done?

In summary, the conversation discusses a qualitative question about work done in the Isothermal Expansion Phase of a Carnot cycle. It is stated that the work done by the engine on the environment during this phase is equal to the energy extracted from the hot reservoir to maintain a constant temperature. However, the person feels that the work should be less and asks if their reasoning is incorrect. The response explains that since the temperature does not change, the heat flow into the gas is equal to the work done, and the work done is represented by the area under the PV graph for the isothermal expansion phase. The conversation concludes with a positive comment about the helpfulness of the website.
  • #1
G01
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Hi. I have a qualitative question about the work done from state 1 to state 2 of a Carnot cycle. This is the Isothermal Expansion Phase. Is work done by the engine on the environment during THIS PHASE ONLY equal to the energy extracted from the hot reservoir to keep the temperature constant. I feel that it should be less. Is my reasoning incorrect?
 
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  • #2
G01 said:
Hi. I have a qualitative question about the work done from state 1 to state 2 of a Carnot cycle. This is the Isothermal Expansion Phase. Is work done by the engine on the environment during THIS PHASE ONLY equal to the energy extracted from the hot reservoir to keep the temperature constant. I feel that it should be less. Is my reasoning incorrect?
Yes.

Since the temperature does not change, the heat flow into the gas is equal to the work done: ([itex]\Delta Q = \Delta U + \Delta W = \Delta U + \int PdV[/itex]; Since [itex]\Delta U = 0, \Delta Q = \int PdV[/itex])

The work done is the area under the PV graph for the isothermal expansion phase. Since the isotherm is T = PV/nR = constant, it is of the form P = K/V where K is constant = nRT. The area under that graph ([itex]\int PdV = K\int dV/V[/itex]) is nRTln(Vi/Vf).

AM
 
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  • #3
Thanks a lot Andrew. Man I love having this website:smile:
 

1. What is the Carnot Cycle?

The Carnot Cycle is a theoretical thermodynamic cycle that describes the most efficient way of converting heat energy into mechanical work. It consists of four stages: isothermal expansion, adiabatic expansion, isothermal compression, and adiabatic compression.

2. What is the isothermal expansion phase of the Carnot Cycle?

The isothermal expansion phase of the Carnot Cycle is the first stage in which the working substance (usually a gas) expands at a constant temperature while absorbing heat from a high-temperature source. This causes the volume of the gas to increase while its pressure decreases.

3. What is the work done during the isothermal expansion phase?

The work done during the isothermal expansion phase is equal to the area under the curve on a pressure-volume (PV) diagram. This can be calculated using the formula W = nRT ln(V2/V1), where n is the number of moles of gas, R is the gas constant, T is the temperature, and V1 and V2 are the initial and final volumes of the gas, respectively.

4. Why is the isothermal expansion phase important in the Carnot Cycle?

The isothermal expansion phase is important in the Carnot Cycle because it allows for the efficient transfer of heat energy into mechanical work. By keeping the temperature constant, the expansion of the gas can occur without any loss of energy due to temperature differences, resulting in maximum work output.

5. How does the efficiency of the Carnot Cycle change during the isothermal expansion phase?

The efficiency of the Carnot Cycle is at its maximum during the isothermal expansion phase. This is because the heat energy absorbed by the gas is converted into work with no loss of energy due to temperature differences. Therefore, this phase has the highest efficiency compared to the other stages of the cycle.

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