# 4.00L of CH4 gas are initially at 20C and 4atm pressure.

1. Sep 13, 2010

### petewil2009

1. The problem statement, all variables and given/known data
4.00L of CH4 gas are initially at 20C and 4atm pressure. Calculate deltaU, deltaH, work and Q(heat) when the sample undergoes each of the following processes, (a) and (b).

a. The gas is expanded isothermally and reversibly to 1atm, after which it is heated at constant pressure to 100C.

b. The gas is heated to 100C under constant pressure, after which it is expanded isothermally and reversibly to 1atm.

2. Relevant equations
The CH4 can be assumed to behave as an ideal gas. The molar heat capacity Cp=34.7 j/molK and may be assumed to be temperature independent.

3. The attempt at a solution

a. part 1 - deltaU = deltaH = 0 because U=Q+W and W=-Q in this case.
W=-Q=nRTln(p2/p1)
n=PV/RT=.00657moles of CH4
W=(.00657moles)(8.314J/molK)(293K)ln(1atm/4atm)=-22.18J??

a. part 2 - deltaH = integral from T1-T2 of nCp(molar heat capacity)delta T.
T1=293K, T2=373K
DeltaH=(.00657moles)(34.7J/molK)(373K-293K)=18.238

DeltaU = nCv(molar heat capacity with constant volume) (T2-T1)
DeltaU = (Cp-R)(t2-T1) = (34.7J/molK-8.314J/molK)(373K-293K) = 2110.88J

deltaU total = ?
deltaH total = ?
work total = ?
Q total = ?

I assume once I get this first part I will be able to complete part b...
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution