# Expansion of an Ideal gas(molecular thermodyanmics)

1. Feb 26, 2010

### casiobeats

I'm having trouble with harder part of this question.

1. The problem statement, all variables and given/known data
One mole of monoatomic ideal gas initially at a pressure of 2.00 bar and temperature of 273 K is taken to a final pressure of 4.00 bar by the reversible path defined by P/V = constant. Calculate the values of Delta(H)(change in enthalpy), Delta(U)(potential energy), q(heat) and w(work). Cv = 12.5 kj*mol^-1*K^-1

2. Relevant equations
Delta(U) = q + w
Delta(U)= Cv*delta(t)
Delta(H)= Cp*delta(t)
Cv = 12.5 kj*mol^-1*K^-1
Cp = Cv - R
w = -Pext*delta(V)
q = Delta(U) - w
R = .08314 dm^3*bar*mol^-1*K^-1

I'm missing the equation for work in this situation as the reversible path is defined by P/V = constant.

3. The attempt at a solution

I found the change in enthalpy and the potential energy. They are correct, the textbook lists quantitative answers. However, the work is proving difficult as I don't understand the reversible path condition(P/V = constant) and how to relate that the energy of work. I know that it relates in some way to the ideal gas equation of state, but I cannot figure out that way. Thank you, I'm not sure if this should be introductory physics or advanced forum, so i've placed it in both.

What i've calculated so far, all are correct according to the text:

Delta(U) = 10.23 KJ*mol^-1
Delta(H) = 17.01 KJ*mol^-1

V1 = 11.35 dm^3
V2 = 22.7 dm^3
T1 = 273 K
T2 = 1092 K

thanks again

2. Feb 26, 2010

### ehild

Hint: plot that reversible path on the P(V) diagram.

ehild

3. Feb 28, 2010

### casiobeats

Okay so if i plot this in PV diagram, i see a linear relationship where both P and V get larger wrt eachother where the linear fit is P=2V. Alright, now this isn't an isothermal process. I cant see how to relate work without that condition. I know there is PdV, but i don't see the next step i guess.

4. Feb 28, 2010

### ehild

P=const * V, but the constant is not 2. Find it. You know the pressure and temperature at the initial state, and have calculated that the volume is 11.35 dm^3. What is P/V?

The work is

$$W = \int_{V1}^{V2}{PdV}$$

P=const*V. Substitute this for P in the integrand.

ehild