4.0 mol of monatomic gas A initially has 9000 J of thermal energy. It interacts

Question

4.0 mol of monatomic gas A initially has 9000 J of thermal energy. It interacts with 3.0 mol of monatomic gas B, which initially has 5000 J of thermal energy. How much heat energy is transferred between the systems as they come to thermal equilibrium? 4.0 mol of monatomic gas A initially has 9000 J of thermal energy. It interacts with 3.0 mol of monatomic gas B, which initially has 5000 J of thermal energy. How much heat energy is transferred between the systems as they come to thermal equilibrium? How much heat energy is transferred between the systems as they come to thermal equilibrium?

Explanation / Answer

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) = (9000J + 5000J) / (4mol + 3mol) = 2000J/mol So the amount of energy transferred between the gases is ?E1 = n1·e' - E1 = 4mol·2000J/mol - 9000J = -1000J So 1000J are transferred from gas 1 to gas 2.

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