Question

2.4 mol of monatomic gas A initially has 5000 J of thermal energy. It interacts with 2.8 mol of monatomic gas B, which initially has 8400 J of thermal energy.

What is the final thermal energy of the gas A?
What is the final thermal energy of the gas B?

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)

= (8400J + 5000J) / (2.8mol + 2.4mol) = 2577 J/mol (answer for both)