# Find the volume and temperature after the isobaric expansion

• Benny
In summary, the question posed is about finding the volume and temperature of air after an isobaric expansion in a non-Carnot engine with specific heat ratio \gamma = 1.40. The asker has attempted to use the ideal gas law and divide the resulting equations to find the pressure after compression, but is stuck on how to incorporate the information about the expansion at constant pressure and the adiabatic process. They also mention that having a P-V diagram would be helpful. Another user suggests using the same procedure for the isobaric process and adding the equation for the adiabatic process, as well as practicing drawing P-V diagrams.
Benny

Q. In a non-Carnot engine, a volume of 100 cm^3 of air, initially at 0 degrees celcius and 1 atm pressure, is compressed isothermally until its volume is 10 cm^3.

The gas is then expanded at constant pressure until its volume and temperature are such that an adiabatic expansion will return the gas to its final state.

The ratio of the molar specific heats of air is $$\gamma = 1.40$$.

Find the volume and temperature after the isobaric expansion.

I really don't know what to do. I'm pretty sure that the question is related to P-V(pressure-volume) diagrams. So I considered the changes in parts.

1. Using PV= nRT for the gas at the start(point 1) and then just after the compression(point 2) and dividing the resulting equations (whilst noting that temperature is constant), I get $$P_1 V_1 = P_2 V_2$$.

Solving for $$P_2$$ I get the pressure of the gas just after the compression to 10 cm^3 as 10 atm.

I can't get much further than this. I find these questions to be slightly easier if I have a P-V diagram to work with but for this question I don't have one. The main problem I have is probably to do with the second paragraph of the question "The gas is then expanded at constant pressure..." I don't really understand how I can use the information in that paragraph.

Any help would be good, thanks.

The main problem I have is probably to do with the second paragraph of the question "The gas is then expanded at constant pressure..." I don't really understand how I can use the information in that paragraph.

You were good when

1. Using PV= nRT for the gas at the start(point 1) and then just after the compression(point 2) and dividing the resulting equations (whilst noting that temperature is constant), I get .

Try making the same procedure for isobaric process. You'll obtain also any equation. Then add equation of adiabatic process.
And it's very useful to learn drawing P-V diagramms. It's not too difficult.

Ok, thanks for the help Yegor.

## 1. What is an isobaric expansion?

An isobaric expansion is a thermodynamic process in which the pressure of a system remains constant while the volume and temperature change.

## 2. How do you find the volume after an isobaric expansion?

The volume after an isobaric expansion can be found using the formula V2 = V1 * T2 / T1, where V1 is the initial volume, T2 is the final temperature, and T1 is the initial temperature.

## 3. How do you find the temperature after an isobaric expansion?

The temperature after an isobaric expansion can be found using the formula T2 = T1 * V2 / V1, where T1 is the initial temperature, V2 is the final volume, and V1 is the initial volume.

## 4. Is an isobaric expansion reversible or irreversible?

An isobaric expansion can be both reversible and irreversible, depending on the conditions under which it occurs. If the expansion is carried out slowly and carefully, it can be considered reversible. However, if the expansion is rapid or there is significant energy loss, it can be considered irreversible.

## 5. What is the significance of isobaric expansion in thermodynamics?

Isobaric expansion is important in thermodynamics because it allows us to study how changes in temperature and volume affect the pressure of a system. It is also commonly used in practical applications, such as in engines and refrigeration systems.

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