Question

2.3 g of helium at an initial temperature of 290 Kinteracts thermally with 7.4 g of oxygen at an initial temperature of 600 K .

a.What is the initial thermal energy of each gas?

b.What is the final thermal energy of each gas?

c.How much heat energy is transferred, and in which direction?

d.What is the final temperature?

Answer 1

a) Internal Energy = Total Translational Kinetic Energy = Number of Particles * Average Kinetic Energy.

Number of Particles, N = (Number of moles, n) * (Avogadro's number, N_a)

Average Kinetic Energy (for a monatomic gas) = (3/2)kT, where k is Boltzman's constant, k = R/(N_a)
For a diatomic gas, Average Kinetic Energy = (5/2)kT (Equipartition Theorem)

n = Mass/(Molecular Mass) = m/M

Internal Energy of He (g)= m/M * (N_a) * (3/2)kT (Helium)
Internal Energy of O2 (g)= m/M * (N_a) * (5/2)kT (Oxygen)

b) Energy gained by cold gas, Q_c = -Q_h, Energy lost by hot gas. Q=mcΔT
(m_helium)(specific heat of helium)(Tf - 300K) = -(m_oxygen)(specific heat of oxygen)(Tf - 600K)
Solve for Tf.
With Tf, you can calculate the final internal energies for the gases and have the answer for d)
c) You can calculate Q_c by plugging Tf from part b). Of course it's in the direction of the hotter gas, Oxygen, to the cooler gas, Helium.
d) Refer to part b) for Tf.

I hope it is helpful.. just plug in the values.