A) MCQ :
Thermodynamics:
Five moles of oxygen gas initially have pressure p = 50 kPa and volume V = 0.25 m3.
What is the initial temperature Ti of the gas?
(a) Ti = 250 K
(b) Ti = 301 K
(c) Ti = 503 K
(d) Ti = 1204 K
The oxygen expands adiabatically and quasistatically to V = 0.75 m3. Its final equilibrium
temperature becomes Tf. What is the ratio Tf /Ti?
(a) Tf /Ti = 0.333
(b) Tf /Ti = 0.481
(c) Tf /Ti = 0.644
(d) Tf /Ti = 0.735
During a reversible adiabatic expansion of an ideal gas, which of the following is NOT true?
A. pV γ = constant B. pV = nRT
C. TV γ−1 = constant D. pV = constant
The latent heat of the water-steam phase transition at p=1 atm and T=100oC is 2256 kJ/kg.
What is the entropy change S as the liquid vaporizes?
(a) –22.56 kJ/K-kg
(b) -6048 J/K-kg
(c) 0 J/K-kg
(d) 6048 J/K-kg
(e) 22.56 kJ/K-kg
An ideal monoatomic gas has a temperature of 350 K at a pressure of 1.5 atm.
What is the density (amount of mol per unit of volume) of the gas?
(a) 0.05 mol/l
(b) 1 mol/l
(c) 6.2 mol/l
(d) Not enough information is given.
An ideal gas of N diatomic molecules has temperature T. If the number of molecules is doubled
without changing the temperature, the internal energy increases by:
A. 0
B. (1/2)NkT
C. (3/2)NkT
D. (5/2)NkT
A real gas undergoes a process that can be represented as a curve on a p-V diagram. The work
done by the gas during this process is:
A. pV
B. p(V2 − V1)
C. (p2 − p1)V
D.  pdV
1) This and the next two questions are related.
An ideal monoatomic gas has a temperature of 350 K at a pressure of 1.5 atm.
What is the density of the gas?
(a) 0.05 mol/l
(b) 1 mol/l
(c) 6.2 mol/l
(d) 15.7 mol/l
(e) Not enough information is given.
What is the average thermal energy of each gas molecule?
(a) 5.21 × 10-30 J
(b) 17.1 × 10-27 J
(c) 2.01 × 10-25 J
(d) 7.25 × 10-21 J
(e) 8.82 × 10-18 J
If the gas were composed of Helium (He) versus Argon (Ar) atoms, what would the ratio of the
average speeds be in the cases? (mHe = 4mp; mAr = 40mp)
(a) VHe / VAr = 10
(b) VHe / VAr = sqrt(10)
(c) VHe / VAr = 1/sqrt(10)
3. There is an ideal gas in a closed container.
If the temperature of the gas is doubled without changing its volume, the average number of gas
molecules striking a wall of the container per unit time is
(a) √2 times as large as that before the temperature is doubled.
(b) 1/√2 times as large as that before the temperature is doubled.
(c) the same as before the temperature is doubled.
(d) twice as large as that before the temperature is doubled.
(e) 1/2 times as large as that before the temperature is doubled.
4. There are two different monatomic ideal gases A and B with the same temperature, pressure
and volume. The mass of atoms in A is twice as large as atoms in B. Which gas contains more
atoms?
(a) A
(b) B
(c) Both contain the same numbers.
5. A monatomic ideal gas in equilibrium at pressure p and temperature T is initially confined in
a volume V/8 by a wall. The wall is suddenly removed and a new equilibrium state is reached.
What is the temperature TF of the final equilibrium state? You may assume that the system is
isolated without any exchange of heat or work with its surrounding environment.
(a) TF = T / 8
(b) TF = T / 4
(c) TF = T / 2
(d) TF = T
(e) TF cannot be determined with the information given.
6. If the work done by an ideal gas as it expands is greater than the heat flowing into the gas, the
temperature of the gas will
(a) rise.
(b) fall.
(c) remain the same.
12. A certain amount (N molecules) of ideal diatomic gas has initial pressure, pi, and initial
volume, Vi, as shown. It undergoes a process (not shown) and ends up with final pressure and
volume, pf and Vf, respectively. Which one of the following statements is true?
13) This and the next two questions are related.
13.1) A heat engine makes use of the thermal cycle shown. The working fluid is 3 grams of
nitrogen, an ideal diatomic gas. There are two isobaric and two isochoric processes:
p1 = 1×106 Pa, p2 = 2×106 Pa
V1 = 500 cm3, V2 = 1000 cm3.
What is the temperature, T, of the gas at point 4 (p1, V1)?
(a) T = 120 K
(b) T = 561 K
(c) T = 842 K
(d) T = 1404 K
(e) T = 1683 K
13.2) How much work, Wby, does the gas do in the 1→2 process?
(a) Wby = -1000 J
(b) Wby = -500 J
(c) Wby = 0 J
(d) Wby = 500 J
(e) Wby = 1000 J
13.3) How much work, Wby, does the gas do in the 2→3 process?
(a) Wby = -1000 J
(b) Wby = 0 J
(c) Wby = 1000 J
14. What is S, the change in the entropy of ten moles of an ideal monatomic gas that is expanded
slowly and isothermally at a temperature of 293K from a pressure of 2 atm to a pressure of 1 atm?
(a) S = 21.7 J/K
(b) S = 57.6 J/K
(c) S = 203.4 J/K
(d) S = 212.6 J/K
(e) S = 841 J/K
15. The latent heat of the water-steam phase transition at p=1 atm and T=100oC is 2256 kJ/kg. What
is the entropy change S as the liquid vaporizes?
(a) –22.56 kJ/K-kg
(b) -6048 J/K-kg
(c) 0 J/K-kg
(d) 6048 J/K-kg
(e) 22.56 kJ/K-kg
Electricity and Magnetism
Charge is distributed uniformly on the surface of a very large flat plate. The electric field at the
distance 2 cm from the plate is 30N/C. The electric field at the distance 4 cm from the plate is:
A. 120N/C
B. 80N/C
C. 30N/C
D. 15N/C
An isolated charged point particle produces an electric field with magnitude E at the distance 2m
from it. At the distance 1m from the particle the magnitude of the field is:
A. E
B. 2E
C. 4E
D. E/2
Give a circular current with radius R and current I. Magnetic induction B of this current creating in
its center is equal:
Two infinitely long straight currents which are parallel and have opposite directions will:
a) attract each other
b) does not interact with each other.
c) repel each other.
d) repulsive force is greater than atractive force.
The potential difference between two points is 100V. If a particle with a charge of 2C is
transported from one of these points to the other, the magnitude of the work done is:
A. 200 J
B. 100 J
C. 50 J
D. 100 J
2. The diagrams show 3 circuits consisting of concentric circular arcs (either half or quarter circles of radii r,
2r, 3r) and radial lengths. The circuits carry the same current. Rank them according to the magnitudes of the
magnetic fields they produce at C, least to greatest.
A. 1, 2, 3
B. 3, 2, 1
C. 1, 3, 2
D. 2, 3, 1
3. A magnetic field exerts a force on a charged particle:
A. always
B. if the particle is moving across the field lines
C. if the particle is moving along the field lines
D. if the particle is at rest
6. A circle wire with a linear charge density  is rotated at a constant angular speed  around its axis.The
magnitude of the magnetic field at the center is:
8. A cyclotron, which is designed to accelerate protons of mass mp = 1.67 × 10-27 Kg to a kinetic energy of
10 MeV, has a radius of 1.20m. The magnitude of the uniform magnetic field B required is,
(a)
(b)
(c)
(d)
(e)
B = 3.33 × 10+1 T
B = 1.09 × 10+1 T
B = 3.0 × 10-1 T
B = 3.8 × 10-1 T
B = 1.7 × 10-1 T
9. The magnetic field B inside a long ideal solenoid is independent of:
a) the current
b) the core material
c) the spacing of the windings
d) the cross-sectional area of the solenoid
e) the direction of the current
10. A solenoid is 3 cm long and has a radius of 0.5cm. It is wrapped with 500 turns of wire carrying a
current of 2A. The magnetic field at the center of the solenoid is
a) 9.9x10-8 T
b) 1.3x10-3 T
c) 4.2x10-2 T
d) 16 T
e) 20 T
12. An electron enters a uniform magnetic field B. The velocity vector of the electron is perpendicular to B
vector (see the figure).
If the velocity of the electron is v1, the electron will move out the magnetic field after t1 (second). If the
velocity of the electron is v2 = 2 × v1, the electron will move out the magnetic field after:
a) t2 = 2 × t1
b) t2 = 0.5 × t1
c) t2 = t1
d) t2 = 4 × t1
13. An electron, which has a mass m and kinetic energy K, enters a space in which there are both electric
field E and magnetic field B. E and B are uniform.
The electric field points vertically upward and the magnetic field points horizontally to the right. The proton
enters with a velocity vector that is perpendicular to both the electric and magnetic fields, and the magnetic
force is opposite to the electric force. To keep the electron moving straight (with no deflection), the
relationship between magnitude of B and E must be:
B. PROBLEMS:
1) A thin rubber rod is charged with a linear charge density λ > 0, then shaped into an arc of angle 60° and
radius R. Determine the electric field magnitude at its center.
Θ -q
2) A system of charge point particles is given in the figure 1. The charge
of particles 1, 2, 3 are +q, -q, +q respectively. Determine:
a) The electric field at the point M.
b) The electric potential at the point M.
c) Potential energy of the system
M

+q

+q
3) Determine the direction and the magnitude of the magnetic field at point O
created by the current I given in the figure 2.
4) 1 mole of an ideal gas follows the cycle shown in the figure 3. 1-2 is isochoric process, 2-3 is adiabatic
process and 3-1 is isobaric process. V1, V2, P1, P2 are given.
Determine:
a) Adiabatic coefficient  and molar specific heats Cv and Cp
2
P2
(from the process 2-3) ?
b) The heats from 1-2 and 3-1 processes ?
c) The thermal efficiency of the engine operating with this cycle.
P1
3
1
V1
Figure 3
V2
5) A Carnot heat engine achieves 33.3% efficiency when
operating between temperatures Th and Tc.
a) Determine the temperature Th if Tc = 270C.
b) If it is operated as a refrigerator operating between the same two reservoirs, how much work, W,
must we supply in order to remove 1 kJ of heat from the cold reservoir.
6) A system of charge point particles is given as shown. The charge of
particles 1, 2, 3 are +q, -q, +q respectively. Determine:
a) The electric field at the point M.
b) The electric potential at the point M.
a
2(-q)
3(+q)
a
1(+q)
7) A Carnot heat engine operates between temperatures Th = 1270C and Tc = 270C.
a) Determine the efficiency of mentioned engine.
b) How much is the power of the engine if 1 kJ of heat per second is supplied from the hot reservoir.
M
8) A solid, infinitely-long, conducting rod has radius a = 15 cm and lies along the z axis. It carries a current
I = 30 A in the +z direction. The current is uniformly distributed across the
rod. It is surrounded, at a distance b = 30 cm, by a thin coaxial conducting
shell that carries a current of the same magnitude, but directed in the -z
direction.
Using Ampere’s Law, determine the direction and the magnitude of the
magnetic field at a distance of:
a) 40 cm from the origin.
b) 20 cm from the origin.
c) 10 cm from the
origin.
Figure 2