Question

2.4 g of helium at an initial temperature of 330 K interacts thermally with 9.0 g of oxygen at an initial temperature of 570 K .

a.) What is the initial thermal energy of each gas? Express your answer using two significant figures. Enter your answers numerically separated by a comma.

b.)What is the final thermal energy of each gas? Express your answer using two significant figures. Enter your answers numerically separated by a comma

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

d.) From helium to oxygen or oxygen to helium?

e.)What is the final temperature? Express your answer using three significant figures and in Kelvin.

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)and (e) Refer to part b) for Tf

I hope it was helpful.. plugin the values ..