Molecular Physics | Thermodynamics Answers

Using Maxwell’s relations, derive the first and second energy equations

3. a) i) Draw a Carnot cycle on p-V diagram. Show that the amount of heat absorbed

(rejected) in a reversible cycle is proportional to the temperature of source (sink).

Using the first law of thermodynamics for an adiabatic process, establish the relation
PV γ = K , where γ is the ratio of heat capacity at constant pressure to that at constant
volume. Plot this equation on a p-V diagram. What will be its slope?

b) Derive an expression for the work done by a gaseous system for an isothermal
expansion of an ideal gas.

Using the partition function for an ideal gas made up of N indistinguishable particles,
obtain Sackur-Tetrode equation.

One mole of an ideal gas expands isothermally to five times its initial volume.
Calculate the entropy change in terms of R, the gas constant.

One mole of an ideal gas expands isothermally to five times its initial volume.
Calculate the entropy change in terms of R, the gas constant.

c) Identify whether the following particles are leptons, baryons or mesons: µ, Λ, η°, π°, p, π+, νe, τ, Σ+, n (

Using the partition function for an ideal gas made up of N indistinguishable particles,
obtain Sackur-Tetrode equation.

.

Calculate the most probable speed, average speed and the root mean square speed for
gas molecules at 300 K. The mass of gas molecule is 5 × 10−26 kg and
kB = 1.38 × 10−23 JK−1
.