Answer to Question #311708 in Quantum Mechanics for Maghesh

Question

A container holds 2 moles of a diatomic gas at temperature T = 420K. At this temperature,

rotational motions (but not vibrational motions) of the gas molecules are allowed.

(a) What is the total internal energy of this gas? (2)

(b) A quantity of energy E = 300 Joules is transferred to the gas. What fraction of this added

energy is responsible for increasing the temperature of the gas? (1)

(c) How much did the internal translational energy increase, and thus how much did the temperature

of the gas increase? (4)

(d) Explain how the predictions from particle statistics fail, when describing the heat capacities

of a diatomic ideal gas.

Answer 1

a)

$Q=\frac 32\nu RT=10470~J,$

b)

$t=\frac EQ=0.029,$

c)

$\Delta T=\frac{2E}{i\nu R}=12~K.$