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Old Dec 2nd 2017, 02:14 AM   #1
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Can't figure out whats wrong with these calculations (Thermal equilibrium)

Hi. I have the following problem and I just can't figure out whats wrong with my calculations.

Problem: You have 2 gasses in a container. Gas A is 2.0g of helium at 300K tempature. Gas B is 8.0g of nitrogen at 600K tempature.

1. Calculate the thermal energies of gasses at initial position.
2. Calculate thermal energies of gasses at thermal equilibrium
3. How much heat is transfered and to what direction
4. What is the final temperature of gasses at thermal equilibrium.

My calcs:

$\displaystyle n_a=\frac{2.0g}{4g/mol}=0.5mol , n_b=\frac{8.0g}{14g/mol}=0.57mol$
1.
$\displaystyle E_{th(a)}=\frac{3}{2}*n*R*T=\frac{3}{2}*(0.5mol)*( 8.31J/mol*K)*(300K)=1869.75J$

$\displaystyle E_{th(b)}=\frac{5}{2}*n*R*T=\frac{5}{2}*(0.57mol)* (8.31J/mol*K)*(600K)=7105.05J$

2.

$\displaystyle E_{f(a)}= \frac{n_a}{n_a+n_b}*E_{tot} = \frac{0.5}{0.5+0.57}*8974.8J=4193.83J$

$\displaystyle E_{f(b)}= \frac{n_b}{b_a+n_b}*E_{tot} = \frac{0.57}{0.5+0.57}*8974.8J=4780.97J$

3.

$\displaystyle Q_1=E_{f(a)}-E_{th(a)}=4193.83J-1869.75J=2324.08J$

$\displaystyle Q_2=E_{f(b)}-E_{th(b)}=4780.97-7105.05J=-2424.08J$

4.

Now this is where I have my problem.

$\displaystyle \Delta$$\displaystyle T_a$=$\displaystyle \frac{Q_1}{\frac{3}{2}*n*R}=\frac{2324.08J}{\frac{ 3}{2}*(0.5mol)*(8.31J/mol*K)}=372.897K$

Now this would indicate that Gas A has higher final temperature than Gas B which just can't be possible, so something is wrong here but I can't just figure out what.
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