Work Done by Gas in Carnot Cycle

In summary, the Carnot Cycle involves both isothermal and adiabatic expansions in which the gas does work and transfers energy. In the adiabatic change, the pressure of the gas expands and requires the use of kinetic energy of the molecules. In the isothermal change, heat energy is transferred to the gas, increasing the pressure and allowing for the same process of pressure acting over a distance and requiring energy. The energy transfer in both cases is from internal energy/kinetic energy to potential energy of the piston. However, in an isothermal process, there can be no change in kinetic energy as temperature must stay constant. In an adiabatic process, the energy must come from the internal kinetic energy of the gas as
  • #1
Peter G.
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Hi,

I was thinking about the isothermal and adiabatic expansions in the Carnot Cycle and I was wondering:

In these processes, the gas is doing work. In the adiabatic change, the pressure (force), acts over a distance (expansion) transferring energy (Kinetic Energy) - but this is an adiabatic change, so it's impossible to transfer energy. Is it therefore, the process of the pressure expanding the gas that requires the use of energy - in this case, the Kinetic Energy of the molecules?

In the case of the isothermal change (I haven't studied the Second Law of Thermodynamics, but from the looks of it, it seems it isn't possible for this change to happen, but, anyway, ignoring that now...) heat energy is transferred to the gas. This thermal energy would increase the K.E, therefore, increasing the pressure and allowing for the same thing to happen - pressure acting over a distance (doing work) and this action requires energy, energy, in this case, Kinetic, which is equal to the amount of thermal energy transferred in: for ∆Q = 0 + ∆W

In those cases, the energy transfer would be from internal energy/KE to potential energy of the piston?

Are those correct?
 
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  • #2
Peter G. said:
In these processes, the gas is doing work. In the adiabatic change, the pressure (force), acts over a distance (expansion) transferring energy (Kinetic Energy) - but this is an adiabatic change, so it's impossible to transfer energy. Is it therefore, the process of the pressure expanding the gas that requires the use of energy - in this case, the Kinetic Energy of the molecules?

Yes. If the gas expands, its temperature has to go down to compensate.

In the case of the isothermal change (I haven't studied the Second Law of Thermodynamics, but from the looks of it, it seems it isn't possible for this change to happen, but, anyway, ignoring that now...)

There's nothing that prevents isothermal change from happening. If I compress a gas, it would ordinarily heat up. However, if I put it in a refrigerator and cool it at exactly the same rate as it's heating up, I can keep its temperature constant.

heat energy is transferred to the gas. This thermal energy would increase the K.E, therefore, increasing the pressure and allowing for the same thing to happen

No, there can be no change in kinetic energy. Isothermal means constant temperature, and temperature is directly proportional to kinetic energy, so kinetic energy can't change in an isothermal process.

What happens is that pressure and volume may change, but temperature has to stay constant. For example, if I compress some gas, but do it slowly enough that the gas is always in thermal equilibrium with its surroundings, I get an isothermal process. Conversely, if I try to expand some gas, its temperature would ordinarily decrease. However, if heat transfer between the gas and its surroundings is efficient enough, the gas can always stay in thermal equilibrium.
 
  • #3
Ah I think I got it:

1. In the isothermal expansion for example, the gas would still, like in the adiabatic, be expanding at the cost of it's internal energy but, at the same time, immediately, energy is flowing in from the surroundings to compensate?

2. During the compressions, I understand the energy transfer. If we imagine ourselves compressing a gas in a piston, we are exerting a force over a distance and transferring chemical energy in our muscles to internal energy in the gas (or is it potential energy to the piston?)

But how does it happen during expansion? The "act" of the pressure acting on the piston over a distance uses up Kinetic Energy? And then the piston gains, say, potential energy?

Thanks once again,
Peter G.
 
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  • #4
Peter G. said:
But how does it happen during expansion? The "act" of the pressure acting on the piston over a distance uses up Kinetic Energy? And then the piston gains, say, potential energy?
During a quasi-static adiabatic expansion, the gas does work on the surroundings in an amount: [itex]W = \int PdV[/itex] where P is the internal pressure of the gas.

If it is not a quasi-static expansion (the external pressure is less than the internal gas pressure by more than an infinitessimal amount), the work done on the surroundings is [itex]W = \int PdV[/itex] where P is the external pressure on the gas (NOT the internal gas pressure).

In both cases, the work is done on the surroundings (e.g. pushing a piston to lift a weight). Since no heat flows into the gas, the energy must come from the internal (kinetic) energy of the gas.

AM
 
  • #5
Hi,

Since no heat flows into the gas, the energy must come from the internal (kinetic) energy of the gas.

Even in an isothermal process?
 
  • #6
Peter G. said:
Even in an isothermal process?
?? An isothermal process is not adiabatic.

In an adiabatic process, dQ = 0. So dU = -dW.

In an isothermal process dQ<>0. So dW <> dU ie. dU = dQ-dW

AM
 

FAQ: Work Done by Gas in Carnot Cycle

1. What is the Carnot cycle?

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

2. How is work done by gas in the Carnot cycle?

Work is done by gas in the Carnot cycle through the expansion and compression of the gas. During the isothermal expansion and compression, the gas expands and contracts while maintaining a constant temperature, and work is done on or by the gas through the movement of the piston. During the adiabatic expansion and compression, work is done by or on the gas as it changes temperature due to the exchange of heat with its surroundings.

3. What factors affect the work done by gas in the Carnot cycle?

The work done by gas in the Carnot cycle is affected by the temperature difference between the hot and cold reservoirs, the amount of gas in the system, and the efficiency of the cycle. A larger temperature difference and greater amount of gas will result in more work being done, while a higher efficiency will result in less work being lost as heat.

4. How does the efficiency of the Carnot cycle relate to the work done by gas?

The efficiency of the Carnot cycle is directly related to the work done by gas. The efficiency is given by the ratio of the work done by the system to the heat supplied to the system. This means that as more work is done by the gas, the efficiency of the cycle increases.

5. What are some real-world applications of the Carnot cycle?

The Carnot cycle is a theoretical concept, but it can be applied to real-world systems such as refrigerators and heat engines. In refrigerators, the Carnot cycle is used to remove heat from the inside of the refrigerator and transfer it to the outside. In heat engines, the Carnot cycle is used to convert heat into mechanical work, such as in steam turbines. It is also used in the study of thermodynamics and the development of more efficient systems.

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