How Does Temperature Change in an Adiabatic Process of a Carnot Engine?

[Chronos000]

Homework Statement

I have to draw a temperature versus entropy for a carnot engine. My solutions say that as a parallel to the PV diagram, the adiabatics on the TS diagram are vertical, going from t2 to t1 and vise versa. My question is really how an adiabatic change results in a temperature change. adiabatic means no heat or out so how can the temperature change at all?

 

[BenR-999]

adiabatic means no heat exchange! yes,
but beware - Heat does not equal temperature! - this is a misnomer that people struggle with due to the common usage in everyday language.

Heat = "transfer' of energy,..but just because there is no transfer doesn't mean the temperature can't change

i.e. take the ideal gas case
$$P_i V_i = nRT_i \qquad P_f V_f = nRT_f$$
$$\Longrightarrow \frac{T_i}{T_f} = \frac{P_iV_i}{P_fV_f}$$

so, by changes P and V we can change temperature, without heat

 

[Andrew Mason]

My question is really how an adiabatic change results in a temperature change. adiabatic means no heat or out so how can the temperature change at all?

Temperature changes because energy must be conserved. That is the first law of thermodynamics: dQ = dU + dW where dQ is the heat flow into the gas, dW is the work done BY the gas and dU is the change in internal energy of the gas.

One can easily see that if dQ = 0 then dU = - dW. That is to say that the change in internal energy of the gas must be of equal magnitude and opposite in sign to the work done by the gas. When a gas expands adiabatically, it does work: dW = PdV. This has to come entirely from the internal energy of the gas since there is no heat flow. So U must decrease. Since internal energy is proportional to temperature for an ideal gas, the temperature must decrease.

AM

 

[Chronos000]

I'm pretty happy with this now thanks. was really the wordplay which confused me

 

[paranormal]

I can provide an explanation for the concept of a Carnot engine and its representation on a T-S diagram. A Carnot engine is a theoretical construct that operates on the principles of thermodynamics, specifically the Carnot cycle. This cycle involves a reversible process of heat transfer and work, and it is represented by a T-S diagram.

On a T-S diagram, the vertical axis represents temperature and the horizontal axis represents entropy. The adiabatic lines on the diagram represent a reversible process in which there is no heat exchange with the surroundings. This means that the system is thermally isolated, and any change in temperature is due to work done on or by the system.

In a Carnot engine, the adiabatic process occurs when the working fluid is compressed or expanded without any heat exchange with the surroundings. This results in a change in temperature without any change in entropy. This is possible because the work done on the system during compression increases the internal energy of the system, leading to an increase in temperature.

Conversely, during expansion, the work done by the system decreases its internal energy, causing a decrease in temperature. This is how an adiabatic process can result in a change in temperature without any heat exchange.

In summary, the adiabatic lines on a T-S diagram for a Carnot engine represent a reversible process in which the temperature changes due to work done on or by the system, rather than heat exchange with the surroundings. This is a fundamental concept in thermodynamics and is crucial for understanding the behavior of idealized systems such as the Carnot engine.