# One mole of neon, a monatomic gas, starts out at STP.

1. Dec 8, 2011

### GabrielleP

1. The problem statement, all variables and given/known data

One mole of neon, a monatomic gas, starts out at STP. The gas is heated at constant volume until its pressure is tripled, then further heated at constant pressure until its volume is doubled. Assume that neon behaves as an ideal gas. For the entire process, find the heat added to the gas.

2. Relevant equations
Q=nc(T2-T1)
PV=nRT
Cp=5/2R
Cv=3/2R

3. The attempt at a solution
Cp=5/2(8.31)=20.775
Cv=3/2(8.31)=12.465
P=3Po=303900 Pa
V=2Vo=44.8*10^-3 m^3
Help?

2. Dec 8, 2011

### GabrielleP

Re: Thermodynamics

Ok, i figured out how to do it. Thanks anyways!

3. Dec 8, 2011

### cepheid

Staff Emeritus
Re: Thermodynamics

Welcome to PF GabrielleP!

Be careful how you write these last two expressions. Right now it's ambiguous whether you mean (5/2)R or 5/(2R). (But of course, we know that it should be the former).

PV = nRT

If V is constant, then we can write

P = (nR/V)*T = (const)*T

in other words, at constant volume, the pressure is just proportional to the temperature (or in other words, the pressure scales linearly with the temperature). This means that if I triple the pressure, I must have tripled the temperature. To illustrate that, start at P0:

P0 = (nR/V)T0

Now if the pressure was tripled, then we now have:

P = (nR/V)*T = 3P0 = 3(nR/V)*T0

So we conclude that the new temperature T = 3T0.

Since you know the change in temperature (T - T0 = 2T0), you can figure out how much heat must have been added to the system using the heat capacity at constant volume, and the appropriate equation.

You would use a similar approach for solving the second part: start with the ideal gas law, and see what happens at constant pressure.