Thermal & Statistical Physics

Use this for “2.00 mol of a diatomic ideal gas at 400 K expands slowly with no heat in or out, from 4 L to 12 L. Find its final temperature and the work it does.”

Use this for “A gasoline engine has a compression ratio of 9.5 and burns fuel to add 2400 J of heat each cycle. With γ = 1.4 for air, find its ideal efficiency, the work per cycle and the heat thrown out.”

Use this for “3.00 mol of helium warms by 40 K. How much heat does it take at constant volume, how much at constant pressure, and how much work does it do at constant pressure?”

Use this for “An Einstein solid of 4 oscillators holds 5 units of energy. In how many ways can the energy be shared, and what is the entropy?”

Use this for “A paramagnet of 10 spins has 7 pointing up. How many microstates have 7 up, and what is the entropy?”

Use this for “A gas in a box with a porous wall that lets molecules through to a big reservoir: which ensemble describes it?”

Use this for “A molecule’s vibration has ħω = 0.12 eV. At 600 K, find Z, the mean number of quanta, the mean energy and the share in the ground level.”

Use this for “Find the thermal wavelength of N₂ (28.01 u) at 77 K. Is nitrogen gas with 10²⁶ molecules per m³ still classical?”

Use this for “Find the most probable, mean and rms speeds of oxygen molecules (32.00 g/mol) at 250 K.”

Use this for “Gold has 5.90 × 10²⁸ free electrons per cubic meter. Find its Fermi energy, Fermi temperature and Fermi speed.”

Use this for “A star’s surface is at 3200 K and its area is 1.5 × 10¹⁷ m². Where does its spectrum peak, and what total power does it radiate?”

Use this for “A cloud of sodium-23 atoms holds 5 × 10¹⁹ atoms per cubic meter. Below what temperature does it form a Bose–Einstein condensate?”