PH202 Recitation Week 06 Problem Set Winter 2015

PH202 Recitation Week 06
Problem Set
Winter 2015
Ryan Scheirer
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Problem 01
If you double the speed of molecules in a gas, by what factor does the pressure change?
Problem 02
What is the rms speed of (a) helium atoms at 2 K, (b) nitrogen molecules at 27◦ C, and (c) mercury atoms
at 100◦ C?
Problem 03
What is the rms speed of an electron at 10, 000K? What fraction of the speed of light is this?
Problem 04
Mars has an atmosphere composed almost entirely of carbon dioxide, with an average temperature of
−63◦ C. (a)What is the rms speed of a molecule in Mar’s atmosphere? (b) What speed would a 1 gram
paper clip have if it had the same average kinetic energy as a molecule in Mar’s atmosphere?
Problem 05
Consider an insulated system consisting of a vacuum cleaner located in a kitchen. Stage (1) Over time
the floor of a kitchen gets quite messy from various food crumbs which are dropped and randomly spread
throughout the kitchen. Stage (2) While vacuuming the kitchen floor you are effectively forcing the
randomly distributed food crumbs into a small container. (a) Rank the change in entropy during each
stage from most positive to least. (b) Do either of these stages violate the second law?
Problem 06
A sample of 50kg of water at 20◦ C is mixed with 50kg of water at 24◦ C. (a) Calculate the final temperature
of the mixture. (b) Rank the change of entropy of each sample of water from most negative to least negative.
(c) Rank the magnitude of the change of entropy of each sample of water from least to greatest.
Problem 07
An engine working at maximum (Carnot) efficiency performs work at the rate of 440kW while using
40800kcal of heat per minute. If the temperature of the heat source is 843K, (a) at what temperature is
the waste heat exhausted? (b) How much exhaust heat is discharged per second?
Problem 08
A nuclear power plant operates at 75% of its maximum theoretical (Carnot) efficiency between temperatures
of 625◦ C and 350◦ C. If the plant produces electric energy at the rate of 7.8 × 1010 min
, how much exhaust
heat is discharged per hour?
Problem 09
A freezer has a COP of 3.8 and uses 200W of power. How long wold it take to freeze an ice-cube tray that
contains 430 grams of water at 10◦ C to 0◦ C.
Problem 10
A heat pump has a COP of 3 and is rated to do work at 1500W . (a) How much heat can this heat pump
add to a room per minute? (b) If the heat pump were turned around to act as an air conditioner in the
summer, what would you expect its COP to be, assuming all else stays the same?
Problem 11
What volume of water at 0◦ C can a freezer make into ice cubes in 1 hour, if the coefficient of performance
of the cooling unit is 7 and the power input is 1 kW?
Problem 12
One mole of monatomic gas is carried around the closed reversible cycle shown below. The pressure
P1 = 1 × 105 P a, the volume V1 = 2m3 and V2 = 8m3 .
(1) Without doing any calculations, determine the sign of ∆W (ii) ∆Q and (iii) ∆E for each segment
of the cycle and the total cycle. Explain your reasoning and present the results in a table.
(a) Calculate the pressure, volume, and temperature of all three points. Present this data in a table.
(b) For each segment of the cycle, calculate (i) ∆W (ii) ∆Q and (iii) ∆E. Present the final results in
a table.
(c)For the complete cycle, what is the TOTAL (i)∆W (ii) ∆Q and (iii) ∆E.
(d) On the figure below, draw arrows for Win ,Wout ,Qin ,Qout for each segment of the cycle.
(e) Is this a heat engine or heat pump?
(f ) Find the efficiency if it is a heat engine or the coefficient of performance if it is a heat pump.
Problem 13
A block of ice with a flat horizontal area of 1m2 lies on the ground. The thickness of the ice block is 1cm.
How long does it take the Sun to melt the block of ice at 0◦ C if (a) the Sun’s rays are perpendicular to the
surface of the block; (b) the Sun’s rays make an angle of 30◦ with the vertical. For both cases assume the
emissivity of ice is 0.050, the average solar energy input is 1000 m
2 and the density of ice is 917 m3 .
Problem 14
A copper rod and an aluminum rod of the same length and cross-sectional area are attached end to end
as shown below. The copper end is held at constant temperature of 250◦ C. The aluminum end is held at
a constant temperature of 0◦ C. Calculate the temperature at the point were the two rods are joined. The
, and for copper 380 smK
thermal conductivity for aluminum is 200 smK
Problem 15
Suppose the insulating qualities of the wall of a house come mainly from a 4in thick layer of brick and an 4in
layer of insulating material. The thermal conductivity of the brick is 0.84 smK
. The thermal conductivity
of the insulating material is 0.03 smK . What is the total rate of heat loss through this wall if the area is
240f t2 and the temperature difference is 12F ◦ ?
Problem 16
A lead bullet traveling at 250 ms penetrates a fence post and comes to rest within the post. If 50% of the
heat generated by friction is absorbed by the bullet, by how much does the temperature of the lead bullet
Problem 17
When a submarine dives down to a depth of 120m, to how large a total pressure is its exterior surface
subjected? The density of seawater is 1030 m
Problem 18
The depth of water at the Hoover Dam is roughly 220m. What is the water pressure (a) at the base of the
dam (b) at a point 110m down from the water surface (c) at a point 55m down from the water surface?
Problem 19
Calculate the difference in pressure that the the blood vessels in a giraffe’s head have to accommodate
as the head is lowered from a full upright position to ground level for a drink. The height of an average
giraffe is about 6m.
Problem 20
A 1m diameter cylindrical vat of liquid is 2m deep. The pressure at the bottom of the vat is 1.3 atm.
What is the mass of the liquid in the vat?
Problem 21
What is the gas pressure inside the box shown in the figure below?
Problem 22
The container shown in the figure below is filled with oil. It is open to the atmosphere on the left. (a)
What is the pressure at point A (b) What is the pressure difference between points A and B? (c) What is
the pressure difference between points A and C?
Problem 23
What volume V of helium is needed if a balloon is to lift a load of 180kg, which includes the weight of the
empty balloon?
Problem 24
A scuba diver and her gear displace a volume of 65L and have a total mass of 68kg. (a) What is the
buoyant force on the diver in sea water? (b) Will the diver sink or float?
Problem 25
The specific gravity of ice is 0.917, whereas that of seawater is 1.025. What fraction of an iceberg is above
the surface of the water?
Problem 26
A foam plastic, with density ρp = 580 m
3 is to be used as a life preserver. What volume of plastic must
be used if it is to keep 20% (by volume) of an 80kg man above water in a fresh water lake? The average
density of the man is ρm = 1040 m
Problem 27
Air flows through the tube shown below. Assume that air is an ideal fluid. (a) What are the air speeds v1
and v2 at points 1 and 2? (b) What is the volume flow rate?
Problem 28
Refer to the figure below.
(a) Without doing any calculations, determine the sign of ∆W (ii) ∆Q and (iii) ∆E for each segment
of the cycle and the total cycle. Explain your reasoning and present the results in a table.
(b) What is the amount of heat extracted from the hot reservoir, QH ?
(c) What is the efficiency of this heat engine?