2.0 mol of monatomic gas A initially has 5000 J of thermal energy. It interacts with 3.0 mol of monatomic gas B, which initially has 8000 J of thermal energy. (4+4 pts.) a. What is the average energy per atom at equilibrium? b. Find the equilibrium temperature.

E_particle = 1,129 10⁻²⁰ J / particle

T = 817.5 K

Explanation:

Energy is a scalar quantity so it is additive, let's look for the total energy of each gas

Gas a

E_a = 2 5000 = 10000 J

Gas b

E_b = 3 8000 = 24000 J

When the total system energy is mixed it is

E_total = E_a + E_b

E_total = 10000 + 24000 = 34000

The total mass is

M = m_a + m_b

M = 2 + 3 = 5

The average energy among the entire mass is

E_averge = E_total / M

E_averago = 34000/5

E_average = 6800 J

One mole of matter has Avogadro's number of atoms 6,022 10²³ particles

Therefore, each particle has an energy of

E_particle = E_averag / 6.022 10²³ = 6800 / 6.022 10²³

E_particle = 1,129 10⁻²⁰ J / particle

For find the temperature let's use equation

E = kT

T = E / k

T = 1,129 10⁻²⁰ / 1,381 10⁻²³

T = 8.175 102 K

T = 817.5 K