Download For simplicity, use g = 10 m/s for this exam.

For simplicity, use g = 10 m/s2 for this exam.
I.
A water reservoir is an elevated water tank that fills with rain water. It can provide a house with its water
supply. In the diagram below, H is the height of the water level as measured from the ground, and h is the
height of the shower head in the bathroom as measured from the ground. (The drawing is not to scale).
water=103 kg/m3
a)
You want to shower. What would happen when you turn on the shower in the bathroom if the reservoir water
level H is equal to the shower height h? Explain.
b) If h=5.0 m, how large must H be in order for you to take a shower in which the exit speed of the water from the
shower head is about 4 m/s (assume that the velocity of the water at the top of the reservoir is negligible)?
c) If you replaced the reservoir with a city water line, what would be the minimum gauge pressure at ground level
so that you could take a shower as described in (b)?
II. One mole of a monatomic ideal gas goes through a thermodynamic cycle consisting of two isobaric
and two isothermal processes. The cycle consists of four parts: 1  2 is isobaric, 2  3 is isothermal,
3  4 is isobaric, 4  1 is isothermal.
P
P1 =
V
Po
P2 =
P3 =
V1 =
V2 =
1
3
Po
V3 =
Vo
2Vo
Pressure (in units of Po)
a) Complete the table to determine the pressure and volume (in terms of Po and Vo ) at each of the four
points 1,2,3,4, and then plot the cycle on the P-V diagram to the right and label the points with their
number.
1.5
1.25
1
0.75
0.5
0.25
0
P4 =
V4 =
0
2
4
6
8
Volume (in units of Vo)
b) If Po=1.01 x 105 Pa and Vo=2.2 x 10-2 m3, determine the minimum and maximum operating
temperatures.
Tmin =
Tmax =
c)
How much work was done in each leg of the cycle and in the whole cycle? (Careful with the signs!)
Cycle leg
1→2
Work done by gas
2→3
3→4
4→1
TOTAL WORK
d) Is the change in internal energy for the full cycle positive, negative, or zero? Explain.
3. A helium-filled balloon has a volume of 1 m3 and can be considered a monatomic ideal gas. As it
rises in the earth's atmosphere, its volume expands without leaking any helium. What will its new
volume (in m3) be if its original temperature and pressure are 20C and 1 atmosphere, and its final
temperature and pressure are –40C and 0.1 atmosphere?
a) 1.5
b) 4
c) 6
d) 8
e) 10
4. An 8.2 kg solid sphere, made of metal whose density is 2100 kg/m3, is suspended by a string. When
the sphere is totally immersed in a liquid of unknown density the tension in the string is 23 N. The
density of the liquid is closest to:
a) 1600 kg/m3
b) 1500 kg/m3
c) 1300 kg/m3
d) 1100 kg/m3
e) 1200 kg/m3
5. The specific heat capacity of steam is 2.09 kJ/kg·ºC, the specific heat of water is 4.18 kJ/kg·ºC, and
the latent heat of vaporization of water is Lv = 2257 kJ/kg.
The heating required to change 1.00 kg of water at 0ºC to steam at 120ºC is approximately
a) 2760 kJ
b) 2510 kJ
c) 2550 kJ
d) 460 kJ
e) 2720 kJ
6. During one cycle, a heat engine exhausts 110 J of thermal energy for every 200 J of thermal energy it
absorbs. What is the efficiency of the engine?
a) 35%
b) 55%
c) 40%
d) 45%
e) 65%
7. This P-V diagram represents a system consisting of a fixed amount of ideal gas that undergoes either
of two different processes in going from state A to state B. (Note: This does not describe a cycle, but
rather two different possible ways of getting from state A to state B.) Which of the following is
TRUE? W1 or W2 represent the work done BY the gas in either process 1 or process 2, respectively.
P
a) W1=W2; Q1=Q2; U1=U2
Process #1
b) W1>W2; Q1>Q2; U1>U2
·
c) W1>W2; Q1>Q2; U1=U2
State A
d) W1>W2; Q1=Q2; U1=U2
·
State B
Process #2
e) W1=W2; Q1<Q2; U1<U2
V
8. You place 1 kg of 0°C ice on a 20°C kitchen counter just long enough for the ice to melt into 0°C
water. Calculate the entropy change (in kJ/K) of the ice, the kitchen counter, and the universe during
the process. Assume that the kitchen counter’s temperature does not change. Lfwater=333.5 kJ/kg
ΔSice
ΔScounter
ΣΔS
a)
-1.2
1.1
-0.1
b)
1.2
-1.2
0
c)
-1.2
1.2
0
d)
1.2
-1.1
0.1
e)
1.2
1.1
2.3