Thermodynamics : Tutorial 1
1. 5 moles of an ideal gas at 400 K and 8 atm pressure undergoes an expansion
isothermally to half the initial pressure. When the expansion takes place
(I)
Irreversibly against ZERO external pressure (Free expansion)
(II)
Irreversibly against 4 atm external pressure
(III)
Reversibly
Calculate the work done ON the gas BY the surrounding.
2. One mole of liquid water is converted to one mole of water vapor at its standard
boiling point of 1000 C under the pressure of 1 standard atmosphere (i.e. 101.325
kPa). Assuming that the molar volume of liquid water is 18 x 10-6 m3 mol-1 , calculate
the work done ON the system by the surrounding during the conversion. Also
assume that water vapor behaves ideally.
3. The decomposition of 1 mole of trinitrotoluene (TNT) at 300 K was studied in a bomb
calorimeter and was found to take place with an isochoric heat change equal to a
change of internal energy ∆𝑈 of -3.3 kJ according to the equation,
C7H5N3O6 (s) + 4 O2(g)
3/2 N2(g)+ 5/2H2(g)+7CO2(g)
Assuming ideal gas behavior for gaseous products and reactants, calculate the
change in enthalpy,∆𝐻.
Solid TNT can be assumed to have a negligible volume relative to other gaseous
components.
4. The enthalpy change accompanying the formation of 1 mole of NH3(g) from its
elements at 300 K is (-) 46.1 kJ. Estimate the change in internal energy assuming
ideal gas behavior for the gaseous phase.
5. Work done on the system when one mole of liquid water is converted to one mole of
gaseous water vapor at 373 K under standard atmospheric pressure is (-) 3.0987 kJ.
If in addition you are told that the heat energy (enthalpy/heat of vaporization of
water) absorbed by the system during this process is 40.82 kJ mol-1. Use the first law
of thermodynamics to calculate the change in internal energy ∆𝑈 of the system.
6. Recapitulate and summarize the conditions under which U will be directly
proportional to T.
7. Calculate the internal energy change that occurs when 10 moles of solid aluminium
are heated from 500 K to 600 K, at constant volume.
C , m = 30J K-1mol-1
8. Recapitulate and summarize the conditions under which H will be directly
proportional to T.
9. Calculate H, when 1 mole H2O at 101 kPa is heated from 353 K to 393 K.
The following data are available,
C p, m (l , H2O ) = 75.0 J K-1mol-1
H vapourization = 47.3 kJ-1 mol-1 at 373 K
C p, m ( , H2O ) = 35.4 J K-1mol-1
10. 2 moles of an ideal monoatomic gas [ Cv,m =3R/2 ,Cp,m =5R/2] at 300 K and 6 atm
pressure (state i) undergoes an expansion adiabatically , to half the initial pressure
(state f) irreversibly against 3 atm external pressure.
Calculate q, ,ΔU, ΔH and w for the process.
11. Consider the adiabatic expansion in the problem 10 above. Suppose it is carried out
reversibly.(i.e. P =Pex) instead of irreversibly (Pex = PB = 3 atm).
Will the final state in the reversible expansion be different to the final state in the
ireversible expansion?
12. What are the conditions under which the three equations,
(I)
𝑃𝑉 𝛾 = 𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡
(II)
𝑇𝑉 𝛾 −1 = 𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡
(III)
𝑃1−𝛾 𝑇 𝛾 = 𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡
can be applied
13. 2 moles of an ideal monoatomic gas [ Cv,m =3R/2 ,Cp,m =5R/2] at 300 K and 6 atm
pressure (state A) undergoes an expansion adiabatically , to half the initial pressure
(state B) reversibly. Calculate q, ΔT,ΔU, ΔH and w for the process.
14. Describe how do you calculate the entropy change ΔS for a given change of state .
15. Show entropy (S) is an extensive property. Give SI units for entropy.
16. Calculate ΔG for the conversion of 10 moles of liquid water to water vapor at its
standard boiling point
17. Ammonium chloride dissolves in water at 270 C with an increase of molar enthalpy
(ΔH) of 34.7 kJ mol-1. The corresponding molar entropy change for the dissolution is
167.1 J K-1 mol-1
(I)
(II)
Calculate the value of ΔG
Determine whether ammonium chloride will spontaneously dissolve in water
at constant temperature and pressure
18. Evaluate the changes in entropy that occurs when 5 moles of an ideal gas are
(I)
(II)
Heated from 270 C to 7270 C at a standard atmospheric pressure
Subject to a tripling of the volume at constant temperature
Cp,mof the gas = 29.1 J K-1 mol-1
19. Calculate the entropy change when 1 mole of an ideal monoatomic gas at 273 K and
101.3 k Nm-2 is heated to 1000 K and compressed to a final pressure of 1013 k Nm-2
20. 2 moles of an ideal monoatomic gas at 300 K and 6 atm pressure undergoes
expansion adiabatically to half the initial pressure reversibly against 3 atm, external
pressure. Calculate q, ΔT, ΔU, ΔH, ΔS and w for the process.
21. 1 mole of liquid water is converted to 1 mole of (gaseous) water vapor at its
standard boiling point 373 K under a pressure of 101.325 k Pa ( 1 standard
atmosphere). The heat energy (enthalpy of vaporization of water) absorbed during
this process is 40.82 kJ mol-1. Calculate the change in entropy for this process