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POWR.03.05.00-00-Z041/17
Example Thermodynamics Problems
(Thermodynamic II year, III semester )
Examples of thermodynamics task
Difference between reversible and irreversible thermodynamically conducted processes.
1. Cylinder of volume Vo = 15,7 dm3 is closed by the piston with no friction movements, the
cylinder is filled with helium under pressure po= 1.5 bar. External pressure po = 1 bar. In the
irreversible isothermal process of expansion the pressure of the gas decreased to the value of
external pressure pk. Calculate amount of heat Q which system should exchange with
surroundings to preserve the Internal Energy change U= 0, (Vo = 15.7 dm3, Po = 1.5 bar, pk= 1
bar. Res: Q = 785 J)
2. Cylinder of volume Vo = 15,7 dm3 is closed by the piston with no friction movements, the
cylinder is filled with helium under pressure po= 1.5 bar. External pressure po = 1 bar. In the
reversible isothermal process of expansion the pressure of the gas decreased to the value of
external pressure pk. Calculate amount of heat Q which system should exchange with
surroundings to preserve the Internal Energy change U= 0, (Vo = 15.7 dm3, Po = 1.5 bar, pk= 1
bar. Res: Q = 955 J)
3. Steel cylinder of volume 40 litters contains argon. Pressure p1 = 10 bar, T1 = 300K. during the
heating process, pressure inside the container increased to the value p2 = 15 bar. Determine the
final temperature, heat delivered do the system (take into account only argon), and internal
energy change U = ?, heat capacity of the argon CV = 12,5 J/molK.
4. Cylinder closed with the piston moving without the frictions, contains 5 moles od neon, the
pressure is 1 bar and temperature T=300K, as a result of heating process, temperature increased
to T2= 400K, molar heat capacity of neon at constant pressure is equal Cp = 20 J/mol K.
Calculate final volume, heat exchanged, and enthalpy and internal energy changes.
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5. Dependence of molar heat capacity at constant volume on temperature for air can expressed by
the equation: Cp = 6.50 + 0.001 T [cal/molK]. Average molar mass of air M = 29g . Calculate:
a) Heat capacity of air in temperature 373K, b) Specific heat capacity of air at T = 673K. c)
how much heat is needed to warm up 10 moles of air from 300 to 400 K
6. 1 dm3 gas mixture at temperature T1 = 293K and pressure 0,986·105 Pa contains 40% volume
of CO and 60% volume of CO2, the gases were heated at constant pressure condition to the
temperature 373 K. Calculate heat needed for that process. Temperature dependence of
Constant-pressure heat capacities of CO and CO2 are expressed by the equations:
Cp (CO) = 6.342 + 1.83·10-3T – 2.80·10-7T2 [cal/mol K]
Cp (CO2) = 6.394 + 10.19·10-3 T – 35,3 ·10-7 T2 [ cal /mol K]
7. Two block of copper were connected. The first, of mass 200 kg had a temperature -40oC,
whereas the second of mass 30 kg had a temperature 380 oC. What will be the final temperature
assuming no heat flow to or from surroundings (res. T = 14,8 oC)
8. 400 kg of ice (of T = 0oC) was added to the 1 tone of water of temperature of 97 oC. What will
be the final temperature. Latent heat fusion of ice = Qmelt = 77,8 cal·g-1. (res. T = 47,06 oC)
9. The container of T=298K is filled with unknown gas (Ar or N2). During the adiabatic
irreversible process of expansion from V1 = 5 dm3 to V2 = 6 dm3 temperature of the system
decreased of 21 K. what is the gas in the container? (answer: nitrogen)
10.10 moles of Hydrogen (p = 1013 hPa, T= 273K) has been warm-up in constant volume
conditions to the Temperature 373 K, and next expanded in the adiabatic process to the volume
1000 dm3, it this process gas did the work pushing the piston charged with constant pressure 10
kPa. Calculate heat transfer (Q), work (W) and the internal Energy (U)
11.Calculate the heat of combustion of 1 mole methanol and 1mole ethanol. Heat of formation of
ethanol, methanol, carbon dioxide, and water (gas) are: 277.84; 238.82; 393.77 and 241.6
kJ∙mol-1 respectively.
12. Calculate the enthalpy of synthesis reaction:
N 2  O2  2 NO
On the basis of heat of the given below reactions:
1
NO  O2  NO2
2
Ho = 56,5 kJ/mol
1
N 2  O2  NO2
2
Ho = 33,9 kJ/mol
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13. Calculate H of reaction:
C2 H 2  H 2 O( c )  CH 3CHO( g )
on the basis of heat of reactions below:
2C  H 2  C 2 H 2
H = + 226.8 kJ·mol-1
1
H 2  O2  H 2 O( c )
2
H =  285.83 kJ·mol-1
C  O2  CO2
H =  393.51 kJ·mol-1
5
CH 3CHO( g )  O2  2CO2( g )  2 H 2 O( g ) H =  1192.25 kJ·mol-1
2
14. Calculate the standard heat of reaction of synthesis of ethane Hx
2C ( s) 3H2( g )  C2 H6( g )  H x
using the heat of appropriate reactions:
C ( s ) O2 ( g )  CO2 ( g )  H1
1
H 2 ( g )  O2 ( g )  H 2 O( c )  H 2
2
7
C2 H 6( g )  O2 ( g )  2CO2 ( g )  3H 2O( c )  H 3
2
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H1 = -393.51 kJ·mol-1
H2 = -285.83 kJ·mol-1
H3 = -1559,84 kJ·mol-1