Answer to Question #81841 in Molecular Physics | Thermodynamics for sedzani

Question

3. A tank of volume 0.3 m3
contains 2 moles of helium gas at 20℃. Assuming the
helium behaves like an ideal gas,
3.1. Find the total internal energy of the system.
3.2. What is the average kinetic energy per molecule?

Answer 1

3.1. The total internal energy of the system calculated by the formula: U=3/2nRT, where n - amount of substance, mole; R - gas constant, R=8.31 J/(K×mol); T – temperature, K. In this case n=2 moles, T=20+273.15=293.15 K. Then: U=3/2×8.31×293.15×2=7308.23 J.

Answer: 7308.23 J.

3.2. Average kinetic energy per molecule calculated by formula: E=3/2 k_BT, where kB – Boltzmann’s constant, kB=1.38×10-23 J/K; T – temperature, K. Then: E=3/2×1.38×10-23×293.15=6.07×10-21 J.

Answer: 6.07×10-21 J.