# Thermodynamics: Piston-Cylinder

## Homework Statement

5kg of nitrogen gas contained in a piston-cylinder arrangement expands in a process, such that pv1.4=p1v11.4, where p1 and v1 are the initial pressure and specific volume, from a pressure of 20 bar to a pressure of 1 bar and a temperature of 300K.

a. What is the initial temperature of the nitrogen?

b. How much work is done by the nitrogen as it expands?

## Homework Equations

I'm not sure which relationships to use or how to even get started for both parts

## The Attempt at a Solution

For part b, we will use the conservation of energy:

U2 + Ke2 + Pe2 = U1 + Ke1 + Pe1 + Q - W

So change in Pe and change in Ke is zero?

Thus, W = U2 - U1 - Q

Last edited:

Redbelly98
Staff Emeritus
Homework Helper
When the gas has "a pressure of 1 bar and a temperature of 300K", what is its volume? Hint: use the equation the relates pressure, volume, and temperature for a gas.

After you get that, you can use

p v1.4 = p1 v11.4

is it just the ideal gas law pV = nRT?

Redbelly98
Staff Emeritus
Homework Helper
Yes.

For part b, this is an adiabatic process, so Q = 0.

Thus, W = -(change in internal energy)?

What should i do with this?

Redbelly98
Staff Emeritus
Homework Helper
There are a couple of ways to calculate W.

It's probably easiest to calculate the internal energy for a diatomic gas at the two temperatures involved (you'll need the right equation for that). Since Q=0, the change in energy gives us W.

Alternatively you can try doing the integral

W = ∫ P dV

So would it be something like: U = (c_v)nRT, where c_v = (5/2)T

Then W = (c_v)nR([change in]T)

Redbelly98
Staff Emeritus