1. TOPIC 10- Thermodynamic (First Law )
Exercise 10 a
1. Fill in the boxes with suitable formula
Process w q ∆U= w + q ∆H= ∆U + ∆(PV) Etc.
Isobaric
Isochoric
Isothermal
reversible
Irreversible
(T not
constant, but
Tinitial =Tfinal )
Adiabatic 1 γ −1
reversible T2 V2  γ −1  P2  γ
=  = 
T1  V1   P1 
Cp
γ = , Cp,m-Cv,m =R
Cv
Adiabatic
irreversible
2. Classify each of the following properties as (a) intensive or extensive , and (b) state function or non state
function ?
(a) Properties Intensive or extensive (b) Properties State function or non
state function
• Mass • w
• V • q
• Cp • Cv
• Cp,m • Cp
• P • U
• T • H
• Molar mass • n
• Density • P
3. Find w, q, ∆U and ∆H if 4 mol of monatomic gas undergoes a constant-pressure expansion from 2 L to 5
L at 0.90 bar.
Process w q ∆U= w + q ∆H= ∆U + ∆(PV)
Isobaric w = -P(V2-V1) Find T1 & T2
= -0.90bar(5-2)L
8.314 J
= -2.7(bar L) × = -273.4 J.
0.0821barL
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2. 4. Find w, q, ∆U and ∆H if 2 mol of He(g) with Cv,m=1.5R undergoes a reversible heating with P going
from 600 torr to 800 torr while V remains fixed at 30 dm3?
Process w q ∆U= w + q ∆H= ∆U + ∆(PV)
V remains 0 P1V1
fixed T1 = =144.24K. T2 = 192.32K
nR
(Isochoric) T2
q = n ∫ C v ,m dT = 2(1.5R )(T2 − T1 )
T1
= 2mol (1.5)(8.314 JK −1 mol −1 )(48.08K )
= 1199.2 J
5. Calculate w, q, ∆U and ∆H if 1.2 mol of a certain perfect gas, undergoes a reversible isothermal
compression at 25 oC from 40.0 L to 28.0 L.
Process w q ∆U ∆H
Isothermal V2 ? 0 0
reversible − nRT ln
V1
 28 
= -(1.2 mol)(8.314 JK-1mol-1)(298K) ln  
 40 
= +1060 J
6. An ideal monatomic gas at 298.15 K and 1 bar is expanded in a reversible adiabatic process to final
pressure of 0.5 bar. Calculate w, q, ∆U and ∆H (each per mole).
Process w q ∆U ∆H
Adiabatic ? 0 γ −1 ?
reversible C p,m 5R / 2 T2  P2  γ
γ = = = 1.667, = 
C v,m 3R / 2 T1  P1 
0.4
 0 .5 
T2 =   (298.15 K ) = 225.96 K
 1 
T2
∆U = n ∫ C v , m dT = n(1.5)(8.314 JK −1mol −1 )(−72.19 K )
T1
= −900.3 J mol −1
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3. 7. A tank contains 20 L of compressed nitrogen at 10 bar and 25 oC. Calculate w, q, ∆U and ∆H when the
gas is allowed to expand reversibly to 1 bar pressure adiabatically. (Cv,m= 20.811 JK-1mol-1)(Ans:-24.1
kJ,0,-24.1 kJ,-33.7 kJ)
8. One mole of an ideal gas expands from 5 to 1 kPa at 298 K. Calculate w and q for a reversible expansion
at constant temperature. (Ans.: -3988 J, +3988 J).
9. Two moles of gas at 100 Pa and 300 K are compressed by use of a constant pressure of 500 Pa. How
much work is done on the gas? (Ans.: +19.95 kJ)
10. A sample consisting of 2 mol of perfect-gas atoms (for which CV,m = 3/2R) is taken through the
cycle shown bellow. (a) Determine the temperature at the points 1, 2, and 3. (b) Calculate q, w, U, and
H for each step and for the overall cycle.
Answer: P/atm V/L T/K Step w/kJ q/kJ ∆U/kJ ∆H/kJ
1 2.00 22.44 273.5 1→2 ? ? w+q qp
2 2.00 44.8 546.9 2→3 0 ? qv ?
3 0.50 44.8 273.5 3→1 ? -w 0 0
Cycle (1→2→3→1) -ve +ve 0 0
11. The molar heat capacity of oxygen at constant pressure for temperatures in the range 300 to 400 K and for
low or moderate pressures can be approximated as Cp,m = a + bT, where a= 25.73 J mol-1K-1 and b= 0.01297
J mol-1 K-2. Calculate w, q, ∆U and ∆H when 2.00 mol of O2 is reversibly heated from 27 oC to 127 oC with
P held fixed at 1.00 atm. Assume perfect-gas behavior.(Ans.:-1.66 kJ, +6.05 kJ, +4.39 kJ, +6.05 kJ)
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4. Exercise 10 b (Objective questions)
1. Which of the following statements is FALSE?
A. w is positive when work is done on the system of interest.
B. w is negative when the system done work on the surroundings.
C. For a thermodynamic process of expansion, wrev < wirrev .
D. For a thermodynamic process of expansion, wrev > wirrev .
E. For a thermodynamic process of compression, wrev < wirrev .
2. Choose the INNCORRECT statement about heat, q.
A. It is a state function.
B. It is an extensive property.
C. The value of q is dependent of the process.
D. For every adiabatic process, q = 0.
E. q is an energy transfer between system and surroundings due to a temperature difference.
Choose the following answers for questions 3-4:
I. A closed system II. An open system
III. An isolated system IV. A system enclosed in adiabatic walls.
3. For which of these systems is/are the system’s matter can exchange with its
surroundings in every process:
A. I B. II C. III D. I & II E. None of the above
4. For which of these systems is/are the system’s energy conserved in every process:
A. I B. II C. III D. I & II E. None of the above
5. An ideal gas is heated slowly and expands reversibly at a constant pressure of P from
a volume of V1 to V2. What are the signs of w and q of the process?
A. +w, + q B. +w, - q C. -w, +q D. -w, - q E. The signs cannot determine.
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