# Piston volume and pressure problem

This seems like it should be really basic, so it's annoying me that I can't figure it out.

## Homework Statement

One cylinder in the diesel engine of a truck has an initial volume of 600 cm^3. Air is admitted to the cylinder at 30 degrees celsius and a pressure of 1.0 atm. The piston rod then does 400 J of work to rapidly compress the air. What are its final temperature and volume?

The answers are 1100 K and 23.9 cm^3

## Homework Equations

In an isobaric process, W = -p delta V
In an isobaric process, V_1 over T_1 = V_2 over T_2

## The Attempt at a Solution

W = -p delta V
400 J = - (600 cm^3 - V_final)

???

Thanks for any help.

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G01
Homework Helper
Gold Member
If you want your answer to come out in SI units (I assume you do, since you are using Joules, an SI unit.) you can't use the pressure in the form of 1.0atm. You have to convert that to Pascals, the SI pressure unit. You will also have to convert the volume measurements to m^3. Your answer will then come out in m^3, which you can convert back to cm^3 if you wish.

You are starting the problem correctly, you just need the right units. Once you get V_f, can you find the final temperature?

Last edited:
Thanks! For some reason I'm still not getting the answer:

400 J = - 101,300 pa (0.0006 m^3 - V_f)
400 = -61 + 101,300V_f
V_f = 0.00455 m^3 = 4550 cm^3

"Once you get V_f, can you find the final temperature?"

Yeah, this part should be easy. V_1 over T_1 = V_2 over T_2

Last edited:
alphysicist
Homework Helper
Hi zzoon,

I don't believe this process is isobaric. When the piston compresses the gas, the pressure will rise to very high levels.

The key point here is that it happens rapidly. If this processes happen rapidly enough, we can treat it as adiabatic.

What does an adiabatic process indicate about the work done? What does it equal to? Once you know that that will guide you to the next step.