MIDTERM I
PHYSICS 6B, SPRING 2009
SCHUMM
PLEASE PUT YOUR NAME ON YOUR EXAM RIGHT AWAY
P = F/A
P/h = g
vA = constant
P + ½ v2 + gy = constant
Q = C T
Q = mcT
H = -kA(T/x)
H = -T/R
R = RA = x/k
P = eAT4
PV = nRT
< ½ mv2 > = 3/2 kT
Q = Lm
 = (V/V)/ T;  = (L/L)/ T
U = Q – W
W
R = x/(kA)
V2
 PdV
V1
Q = W = nRT ln(V2/V1)
PV = constant; TV-1 = constant;  = CP/CV
C = (1/n) (U/T)
e = W/Qh = 1 – (Qc/Qh); Qh = W + Qc
ecarnot = 1 – (Tc/Th); Qc/Qh = Tc/Th
S = Q/T
g = 9.8 m/s2
 = 5.67 x 10-8 W/(m2K4)
k = 1.38 x 10-23 J/K = Boltzmann Constant cwater = 4184 J/(kg-K)
Heats of Transformation for Water:
Lmelt = 334 kJ/kg
0 C = 273.2 K
TF = (9/5)TC + 32
1 Atm = 101.325 kPa
R = NAk = 8.314 J/K
Lboil = 2257 kJ/kg
Problem 1 [5 Points Each; No Partial Credit] NAME: ________________________
Please clearly indicate your answer by circling the letter (a), (b), (c), etc., of the choice
you make.
1.1 During a thermodynamic process, an system under observation loses entropy. Which
one of the following is true about the environment surrounding the system?
(a) Its entropy stays the same
(b) Its entropy increases
(c) Its entropy decreases
(d) There is not enough information to choose any of the above.
1.2 An ideal gas has initial pressure, temperature, and volume of P, T, and V. The volume
is increased by a factor of two within losing or adding any gas. What can you say about
the temperature of the gas?
(a) The temperature doubles
(b) The temperature is reduced by half
(c) The temperature remains the same
(d) There is not enough information to choose any of the above.
1.3 An object of three times the density of water is held submerged in a tank of water and
released. What can you say about the magnitude of the net force on the object the instant
after it’s released and begins to sink to the bottom of the tank?
(a) The magnitude of the net force is greater than the weight of water it displaces
(b) The magnitude of the net force is equal to the weight of the water it displaces
(c) The magnitude of the net force is less than the weight of water it displaces
1.4 An ideal gas at temperature T is composed of one mole of helium and one mole of
argon. An argon atom is much more massive than a helium atom. Which of the following
is true?
(a) The mole of argon contains more random kinetic energy (heat) than the mole
of helium.
(b) The mole of argon contains less heat than the mole of helium.
(c) The mole of argon contains them same amount of heat as the mole of helium.
1.5 Water flows downwards through a pipe that increases to a steadily larger diameter as
it slants downward. As you follow the flow downward, the pressure
(a) Increases
(b) Decreases
(c) Can’t say – depends on the slope of the pipe and on how fast the pipe opens up
as you go down.
Problem 2 [25 Points]
An insulated vat (one for which no heat can enter or leave) contains 1000 grams of water
at exactly the boiling point (100 C). 20 grams of ice at exactly the freezing point (0 C) is
dropped into the vat. The heat of transformation for melting ice and the specific heat of
water can be found on the formula sheet.
(a) How much heat is needed to melt the ice without raising the temperature of the water
that remains in the vat after the ice is melted?
(b) If the water from the ice didn’t mix at all with the rest of the water in the vat, what
would the temperature of the rest of the water in the vat be just after the melting the ice
(but not raising the temperature of the water that came from the melted ice)?
(c) Of course, the water in the vat will heat up and mix with the water from the ice. What
is the temperature of the water in the vat (original 1000 grams plus the 20 grams from the
melted ice) after everything comes into equilibrium?
Problem 3 [25 points]
In the following, to make your work easier, please assume that the acceleration g due to
gravity is exactly 10 m/s2. Remember that the weight of an object, in Newtons, is given
by w = mg. where m is the object’s mass. Also assume that the density of water is exactly
1 g/cm3.
A cylindrical glass dish of cross-sectional area 20 cm2 and height 8 cm, and negligible
mass, floats on the surface of a bucket of water.
(a) If you press on the bottom of the dish so that it becomes half-submerged (4cm of the
height of the dish remains above the level of the water), what mass of water is displaced
by the dish?
(b) You have a collection of fishing sinkers, each of which weighs 0.3 Newton (a bit
more than an ounce). What is the minimum number of sinkers that you need to put into
the dish in order to sink it? (You are not pressing on the dish anymore when you start to
put the sinkers in.)
Problem 4 [25 Points]
The left end of a 10m long aluminum shaft is fixed, and the right end pushes on a
frictionless plunger that forms the left end of a cylinder of gas (see diagram). The gas
volume inside the cylinder has cross-sectional area of 0.1 m2 and a depth of 10cm, and
contains an ideal gas at 0.5 atmosphere. The entire system is in thermal equilibrium at
0C .
If the thermal coefficient of linear expansion of the aluminum shaft is 2.5x10-5, what will
the pressure of the gas be after the entire system (shaft plus gas cylinder) is raised to a
temperature of 100 C?