Question

4 mol of monatomic gas A interacts with 3 mol of monatomic gas B. Gas A
initially has 8000 J of thermal energy, but in the process of coming to thermal equilibrium it
transfers 2000 J of heat energy to gas B. How much thermal energy did gas B have
initially?

Answer 1

The internal energy of an ideal gas is given by:
E = n?Cv?T
or in terms of molar energy:
e = E/n = Cv?T

For a monatomic ideal gas Cv = (3/2)?R, i.e. it is the same for the two gases. Therefore the gas samples have the same molar energy in equilibrium. Let's call this value e'

Use this to balance initial energy and energy in equilibrium:
E1 + E2 = (n1 + n2)?e'
=>
e' = (E1 + E2) / (n1 + n2)
= (8000J + 2000J) / (4mol + 3mol) = 1428.57 J/mol

So the amount of energy transferred between the gases is
?E1 = n1?e' - E1 = 4mol*1428.57J/mol - 8000J = -2285.71J

So 2285.71 J are transferred from gas 1 to gas 2