Physics 1310
Key

Practice Exam 1
1. A chemistry student heats a 200 gm aluminum rod to 200ºC. The rod is 10.00 cm long. She then
drops the rod into an insulated container holding 500 gm of water at 10ºC. When the water and the
aluminum rod come to equilibrium, by how much has the length of the rod changed? Note: The
coefficient of linear expansion for aluminum equals 24x10-6 ºC –1 and the specific heat of aluminum
equals 900 J/kg ºC. The specific heat of water equals 4186 J/kg ºC.
First we need to get the final T:

0.200 kg x 900 J/kg ºC x (200ºC – T) = 0.500 kg x 4186 J/kg ºC (T – 10ºC)
T = 25ºC
Now, calculate L:
L = 24x10-6 ºC –1x 10.00 cm x (25ºC – 200ºC) = - 0.042 cm
2. A physics professor puts 2 moles of nitrogen gas into a container at 100 K. The absolute pressure
inside the container equals 1.00 atmospheres. He then heats the gas by an isochoric process until the
temperature of the gas equals 300K. What is the absolute pressure in the container now?
Ideal Gas:
pV/T = constant. Here V = constant. So p/T = constant  p = 300 K/100 K x 1.00 atm = 3.00 atm
3. A geoscience student puts 2 moles of air into a container at 300 K. She wants to heat the gas to a
temperature so that the rms speed of CO2 equals 1000 m/s. To what temperature should she heat the
gas? Note: the molar mass of CO2 equals 44 gm/mol.
v = sqrt( 3 kT / m) = sqrt (3RT/M) 
T = M x v2 / 3R = 44x10-3 kg / mol x 1.000x106 m2/s2 / 24.9 J/mol-K = 1767 K = 1.8 x103 K
4. A biology student places 100 g of ice at -30C into a very well insulated container that holds 600 g of
water at 80C. Calculate the temperature of this system when it comes to equilibrium. Note: The
specific heat of ice equals 2090 J/kg ºC, the specific heat of water equals 4186 J/kg ºC, and latent heat of
fusion of water equals 333 J/g.
100 g * 2.090 J/g ºC * 30ºC + 100 g *333 J/g + 100 g * 4.186 J/g ºC * T = 600 g * 4.186 J/g ºC * (80ºC – T)
 T = 55 ºC
5. A field biologist is using an insulated container with dimensions equal to 20 cm x 20 cm x 20 cm.
(The total surface area of the exterior container walls equals 0.240 m2.) The thickness of the container
walls equals 3.00 cm. The thermal conductivity of the container material equals 0.040 W/m-K. The
temperature outside the container equals 20°C. She places 500 g of ice at 0ºC inside the container. How
long will it take for all the ice in the container to melt? Note: The specific heat of ice equals 2090
J/kg ºC, the specific heat of water equals 4186 J/kg ºC, and latent heat of fusion of water equals 333 J/g.
H = 0.040 W/m-K * 0.240 m2 * 20ºC / 0.03 m = 6.4 W
6.4 W * time = 500 g * 333 J/g = 1.67 x105 J  time = 7.2 hours
6. A tungsten filament with surface area equal top 8.0x10-5 m2 and emissivity equal to 0.25 has
temperature equal to 3000K and is in an environment with temperature equal to 300K. How much
power does this filament radiate? Note: The Stefan-Boltzmann constant equals 5.67x10-8 W/m2 K4.
P = 0.25 * 5.67x10-8 W/m2 K4 * 8.0x10-5 m2 * [(3000 K)4 - (300 K)4] = 92 W
7. Consider 2.00 moles of an ideal gas at atmospheric pressure and 300 K. The specific heat at constant
volume of this gas equals 12.5 J/mol ºC. As 200 J of heat enters the gas, it undergoes an isobaric
expansion. Calculate the change in the internal energy of the gas during this process.
Cp = Cv + R = 20.9 J/mol ºC
Q = 200 J = 2.00 mol * 20.9 J/mol ºC * T  T = 4.78 ºC
U = 2.00 mol * 12.5 J/mol ºC * 4.78 ºC = 120 J
8. Consider 2.00 moles of an ideal gas at atmospheric pressure and 300 K. The specific heat at constant
volume of this gas equals 12.5 J/mol ºC. The gas goes through a cycle, returning to the initial conditions.
During this cycle, 500 Joules of heat enters the gas from a reservoir at 600K and 400 Joules of heat
leaves the gas and flows into a reservoir at 300K. Calculate the amount of work done by the gas in
this cycle.
W = QH – QC = 100 J
9. A heat engine takes in 50 kJ of heat from the hot reservoir and transfers 30 kJ of heat into the cold
reservoir. Calculate the efficiency of this engine.
W = 20 kJ
eff = 20 kJ / 50 kJ = 40%
10. A heat engine operates between a hot reservoir at 100ºC and a cold reservoir at 0ºC. Calculate the
maximum possible theoretical efficiency of this engine.
effcarnot = 100 K / 373 K = 27%
11. A 200 g ice cube with temperature equal to 0ºC is placed in a large tank of water with temperature
equal to 27ºC. Calculate the change in entropy of the water in the tank as this system comes to
equilibrium.
S = Q/T = -(200 g * 333 J/g+200g*4.186J/gºC*27ºC) / 300K = - 297 J/K
12. In the diagram, q1 = 5.0 C, q2 = -5.0 C, q3 = 5.0 C, and
d = 30 cm. Calculate the net force that q2 and q3 exert on q1.

q2
F = 9x109 * (25x10-12 /9 x10-2 - 25x10-12 /36 x10-2) N
= 1.88 N (to the right)
13. In the diagram, q1 = 5.0 C, q2 = -5.0 C, and d = 30 cm.
Calculate the electric field at point P.
E = 9x109*(-5x10-6 /9 x10-2-5x10-6 /9 x10-2)N/C
= 1.0x106 N/C (to the left)

d
d
+
q1
+
q3
d
d
q2
+
q1
P
14. A small sphere with mass equal to 50 g has a charge equal to 6.00x10-6C.
The sphere is suspended by a massless string and placed in a uniform electric
E
field. The equilibrium position of the sphere is shown in the figure to the
right. Calculate the magnitude of the electric field.
mg / cos(36.9º) = qE / sin(36.9º)  E = (mg /q) tan(36.9º) = 61,000 N/C
+
36.9
E
15. In the diagram to the right, the
magnitude of the electric field equals
12,000 N/C. Calculate the change in
electric potential as a positively charged
particle with charge equal to 5.0 C
moves from point A to point B.
V = - E y
= - 12,000 N/C * 0.04 m = - 480 volts
8
B
6
y(cm)
E
4
E
E
E
2
A
0
0
2
4
6
8
10
12
14
x(cm)
16. In the field described in problem 15, a proton (m = 1.67x10-27 kg and q = e =1.60x10-19 C) is released
from rest at point A. What is the speed of this particle when it hits one of the plates?
KE = ½ mv2 = -q V 
v = sqrt (-2 q V / m) = sqrt ( 2 * 1.60x10-19 C * 720 V / 1.67x10-27 kg) = 3.7x105 m/s
17. A parallel plate capacitor is composed of two plates; the surface area of one side of each plate equals
0.50 m2. These plates are separated by 1.0 micrometers. The electric potential difference between these
two plates equals 2000 volts. The space between the plates is filled with a substance with dielectric
constant equal to 100. Calculate the magnitude of the charge stored on each plate of this
capacitor.
C = 100 * 8.85x10-12 C2/N-m2 * 0.50 m2 / 1.0x10-6 m = 443 F
Q = 443 F * 2000 V = 0.885 C
18. The resistivity of tungsten equals 5.6x10-8 -m. Calculate the electrical resistance of a tungsten
filament with diameter equal to 0.020 mm and length equal to 20 cm.

the power dissipated in the light bulb.
R
+
R = 5.6x10-8 -m * 0.20 m / [3.14 * (1.0x10-5 m)2] = 36 

19. In the circuit, the battery emf equals 9.0 volts, the volatage
drop across the series resistor equals 3.0 volts and the
resistance of the series resistor, Rs, equals 10.0 . Calculate
s

I = 3.0 volt /10.0 = 0.30 amp
-
V = 6.0 volt
P = 1.8 Watt
20. For the circuit,  = 18.4 volts, Rd = 10.0 K , C =10.0 F. The
capacitor is initially fully charged and the switch moves from c to d at
time t = 0.00.
Calculate the current flowing through Rd at t = 0.10 seconds.

RC = 0.100 sec
VC = 18.4 volt * e-1 = 6.77 volt
I = 6.77 volt / 10 k = 0.677 mA
Rc

c
d
+
sw itc h
+
-
Rd
-
C