# Temperature change in an isentropic flow of an ideal gas

• citrouille
In summary, an isentropic process in the flow of an ideal gas is one that is both reversible and adiabatic. This means that there are no losses to friction and no heat transfer with the surroundings. However, in cases where a temperature gradient occurs within the gas, there may be some heat transfer within the gas itself. This heat transfer is not significant enough to affect the overall process, making it still considered adiabatic.

#### citrouille

I am a bit confused by the definition of an isentropic process in the flow of an ideal gas.

for a process to be reversible, there are no losses to friction (viscosity in this case),
for a process to be adiabatic, there is no heat transfer with the surroundings.

That being said, when a compressible gas flows through a nozzle, there is a temperature change. When this happens, a temperature gradient occurs. Where there is a temperature gradient, heat transfer occurs within the gas. I was always taught that, according to the 2nd principle of thermodynamics, a heat transfer due to a temperature gradient (from hot -> cold areas) is irreversible...which is directly contradicting the definition of a reversible & adiabatic flow...

Hope this is a pertinent question...

Thanks a lot for any help.

citrouille said:
I am a bit confused by the definition of an isentropic process in the flow of an ideal gas.

for a process to be reversible, there are no losses to friction (viscosity in this case),
for a process to be adiabatic, there is no heat transfer with the surroundings.

That being said, when a compressible gas flows through a nozzle, there is a temperature change. When this happens, a temperature gradient occurs. Where there is a temperature gradient, heat transfer occurs within the gas. I was always taught that, according to the 2nd principle of thermodynamics, a heat transfer due to a temperature gradient (from hot -> cold areas) is irreversible...which is directly contradicting the definition of a reversible & adiabatic flow...

Hope this is a pertinent question...

Thanks a lot for any help.

Imagine a bunch of balloons containing gas. Imagine that they expand when they fly out of a window. The expansion of the gas cools the gas in the balloons. Yet, there is not any significant heat exchange between the balloons. That's because there's not enough time permitted for that exchange of heat to be significant. Thus, it is adiabatic.

kmarinas86 said:
Imagine a bunch of balloons containing gas. Imagine that they expand when they fly out of a window. The expansion of the gas cools the gas in the balloons. Yet, there is not any significant heat exchange between the balloons. That's because there's not enough time permitted for that exchange of heat to be significant. Thus, it is adiabatic.

I do not have a problem with the fact that the process is adiabatic (no heat transfer with the surroundings). My problem is with the fact that the transformation is reversible, and yet there is a spatial temperature gradient which would cause heat transfer within the gas (not with the surroundings). Heat transfer due to a temperature gradient within the gas is irreversible...maybe I'm thinking too much...sorry

citrouille said:
kmarinas86 said:
Imagine a bunch of balloons containing gas. Imagine that they expand when they fly out of a window. The expansion of the gas cools the gas in the balloons. Yet, there is not any significant heat exchange between the balloons. That's because there's not enough time permitted for that exchange of heat to be significant. Thus, it is adiabatic.

I do not have a problem with the fact that the process is adiabatic (no heat transfer with the surroundings). My problem is with the fact that the transformation is reversible, and yet there is a spatial temperature gradient which would cause heat transfer within the gas (not with the surroundings). Heat transfer due to a temperature gradient within the gas is irreversible...maybe I'm thinking too much...sorry

If you count the separate balloons as members of the same "gas", you can easily see how there is not significant transfer of heat, not even between parts of the gas.

kmarinas86 said:
If you count the separate balloons as members of the same "gas", you can easily see how there is not significant transfer of heat, not even between parts of the gas.

That makes more sense ! Thanks a lot for clearing that up.

## 1. What is an isentropic flow?

An isentropic flow is a flow in which there is no change in entropy. This means that the flow is adiabatic (no heat exchange) and reversible (no energy losses). In other words, the total energy of the flow remains constant.

## 2. How does temperature change in an isentropic flow?

In an isentropic flow of an ideal gas, the temperature changes due to changes in pressure and volume. As the gas expands, it does work on its surroundings, causing a decrease in temperature. Conversely, as the gas is compressed, work is done on the gas, leading to an increase in temperature.

## 3. What is an ideal gas?

An ideal gas is a hypothetical gas that follows the ideal gas law, which states that the pressure, volume, and temperature of the gas are directly proportional to each other. This means that as one variable increases, the others also increase in proportion, assuming constant moles and temperature.

## 4. How does temperature change affect the properties of an ideal gas?

As the temperature of an ideal gas increases, the average kinetic energy of the gas molecules also increases, leading to an increase in pressure and volume. Additionally, the gas molecules will move faster and collide more frequently, resulting in an increase in the rate of diffusion and effusion.

## 5. What factors can affect temperature change in an isentropic flow of an ideal gas?

The temperature change in an isentropic flow of an ideal gas can be affected by the initial temperature, pressure, and volume of the gas, as well as the specific heat capacity of the gas. Additionally, external factors such as heat transfer, friction, and non-ideal behavior of the gas can also impact the temperature change in the flow.