Thermodynamic Homework 1 CM2133 (2025)
Question 1 (10 points)
Read a thermodynamic table to find the values of the standard enthalpy of
formation ∆𝑓𝑓 𝐻𝐻∅ for the following substances:
a) Liquid water
b) Water vapour
c) Carbon (graphite)
d) Carbon (diamond)
e) Hydrogen gas
f) Oxygen gas
g) Carbon dioxide gas
h) Methane gas
Calculate ∆𝐻𝐻∅ following processes:
i) condensation of steam
j) allotropic conversion of graphite to diamond
k) combustion of carbon in oxygen
𝐶𝐶(𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔ℎ𝑖𝑖𝑖𝑖𝑖𝑖) + 𝑂𝑂2 (𝑔𝑔𝑔𝑔𝑔𝑔) → 𝐶𝐶𝑂𝑂2 (𝑔𝑔𝑔𝑔𝑔𝑔)
l) combustion of methane in oxygen to form liquid water
𝐶𝐶𝐻𝐻4 (𝑔𝑔𝑔𝑔𝑔𝑔) + 2𝑂𝑂2 (𝑔𝑔𝑔𝑔𝑔𝑔) → 𝐶𝐶𝑂𝑂2 (𝑔𝑔𝑔𝑔𝑔𝑔) + 2𝐻𝐻2 𝑂𝑂(𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙)
Question 2 (10 points)
You have an equimolar mixture of nitrogen and oxygen at pressure of
101325 𝑁𝑁𝑚𝑚−2 and a temperature of 300 𝐾𝐾. Assuming that nitrogen and
oxygen behave as ideal gases at this temperature and pressure, calculate:
a) the volume of the one mole of the gas mixture
b) the internal energy per mole of the gas mixture
c) the average translational kinetic energy of each molecule
d) the root-mean-square speed of the nitrogen molecules
e) the root-mean-square speed of the oxygen molecules
Question 3 (10 points)
One mole of a monatomic ideal gas initially at state 0 with 𝑃𝑃0 = 5 𝑏𝑏𝑏𝑏𝑏𝑏 and
𝑇𝑇0 = 300 𝐾𝐾 undergoes a three-step cyclic process:
i) It is reversibly and isochorically cooled to state 1 with a temperature of
𝑇𝑇1 = 150 𝐾𝐾, a pressure of 𝑃𝑃1 𝑏𝑏𝑏𝑏𝑏𝑏 and volume 𝑉𝑉1 .
ii) It is then expanded reversibly and isothermally to state 2 with a pressure
of 𝑃𝑃2 𝑏𝑏𝑏𝑏𝑏𝑏 and a volume of 𝑉𝑉2 𝑚𝑚3 .
iii) It is then reversibly and adiabatically compressed from state 2 back to
state 0 at the initial pressure of 5 𝑏𝑏𝑏𝑏𝑏𝑏 and the initial temperature of
300 𝐾𝐾.
Calculate
a) the initial volume 𝑉𝑉0 .
b) Calculate the pressure 𝑃𝑃1 at state 1.
c) For the process ii), write an equation relating 𝑃𝑃2 and 𝑉𝑉2 to 𝑃𝑃0 and 𝑉𝑉0 .
d) For the process iii), write an equation relating 𝑃𝑃2 and 𝑉𝑉2 to 𝑃𝑃0 and 𝑉𝑉0 .
e) Solve your equations in c) and d) to calculate 𝑃𝑃2 and 𝑉𝑉2 .
Question 4 (20 points)
One mole of a diatomic ideal gas at 298.15 𝐾𝐾 is expanded from 5 𝑏𝑏𝑏𝑏𝑏𝑏 to 1 𝑏𝑏𝑏𝑏𝑏𝑏
in three ways.
i) reversibly and isothermally
ii) isothermally against an external pressure of 1 𝑏𝑏𝑏𝑏𝑏𝑏
iii) irreversibly and adiabatically against zero external pressure
In each case, calculate the following quantities (in any order of calculation)
a) ∆𝑄𝑄, the heat gained by the gas
b) ∆𝑊𝑊, the work done on the gas
c) ∆𝑈𝑈, the change in the internal energy of the gas
d) ∆𝐻𝐻, the change in the enthalpy of the gas
e) ∆𝑆𝑆𝑠𝑠𝑠𝑠𝑠𝑠 , the change in the entropy of the gas
f) ∆𝑆𝑆𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 , the change in the entropy of the surroundings
g) ∆𝑆𝑆𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢 , the change in the entropy of the universe
Question 5 (10 points)
A heat engine is run between the environmental temperature of 303.15 𝐾𝐾 and
a geothermal source producing 100 𝑘𝑘𝑘𝑘 𝑚𝑚𝑚𝑚𝑚𝑚−1 of water at 90 ℃. Calculate
a) the maximum efficiency of the heat engine operating between these
temperatures
b) the maximum amount of useful work that can be obtained from this
heat engine per minute
c) the minimum amount of heat lost to the environment
d) the minimum increase in the entropy of the environment
Question 6 (10 points)
A piece of iron of mass 4 𝑘𝑘𝑘𝑘, heat capacity 25 𝐽𝐽𝐾𝐾 −1 𝑚𝑚𝑚𝑚𝑚𝑚 −1 and temperature
0 ℃ is equilibrated with 1 𝑚𝑚𝑚𝑚𝑚𝑚 of water vapour at 100 ℃ in an isolated
container which is at a constant pressure of 1 𝑎𝑎𝑎𝑎𝑎𝑎.
At equilibrium all the water condensed to liquid and the temperature is
uniform throughout.
Look up the relevant properties of water in any standard source of
thermodynamic data.
Calculate:
a) the equilibrium temperature
b) the entropy change of the metal
c) the entropy change of the water
d) the entropy change of the system