University Physics with Modern Physics Plus Mastering Physics with eText -- Access Card Package (14th Edition)
14th Edition
ISBN: 9780321982582
Author: Hugh D. Young, Roger A. Freedman
Publisher: PEARSON
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Chapter 20, Problem 20.40P
CP As a budding mechanical engineer, you are called upon to design a Carnot engine that has 2.00 mol of a monatomic ideal gas as its working substance and operates from a high- temperature reservoir at 500°C. The engine is to lift a 15.0-kg weight 2.00 m per cycle, using 500 J of heat input. The gas in the engine chamber can have a minimum volume of 5.00 L during the cycle. (a) Draw a pV-diagram for this cycle. Show in your diagram where heat enters and leaves the gas. (b) What must be the temperature of the cold reservoir? (c) What is the thermal efficiency of the engine? (d) How much heat energy does this engine waste per cycle? (e) What is the maximum pressure that the gas chamber will have to withstand?
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As shown in the figure, a container with a moveable piston and containing a monatomic ideal gas in an initial state A undergoes an isovolumetric, then an isothermal, and finally an isobaric process to complete the cycle.
P (atm)
C
V (L)
0
When the gas is in the initial state, the volume is 7.00 L, the pressure is 3.00 atm, and the temperature is 350 K. The gas is first warmed at constant volume to a pressure of 4 times the initial value (state B). The gas is then allowed to expand isothermally to some
new volume (state C). Finally it is compressed isobarically to its initial state. (Due to the nature of this problem, do not use rounded intermediate values in your calculations-including answers submitted in WebAssign.)
(a) Find the number of moles of the gas.
moles
(b) Find the temperature of the gas at state B (in K).
K
(c) Find the temperature of the gas at state C (in K).
K
B
A
a) Consider a process involving an ideal diatomic
gas with n = 3mol, following p = aV, where
a = 1 x 105 Pa/m³ is a constant. The gas ex-
pands from volume V; = 1 m³ to V; = 4m3.
P2
Find the
(i) work done on the gas.
(ii) heat entering the gas.
1
(iii) change in the internal energy of the gas.
b) Now consider the cycle depicted in the figure,
involving the same amount of gas as in the
previous part. A → B is the process described
in the previous subtask, B → C an isochor and
C → A an isobar. Additionally, V2/V1 = n = 4
and Vi = 1 m³. Find the
Pi
3
i) work done by the gas during one loop of
the cycle.
V1
V2
V
ii) thermal efficiency of the cycle.
iii) maximum theoretical efficiency of a Car-
not cycle having the same temperature
extrema as in this cycle.
iv) coefficient of performance of the cycle, if
it were used as a refrigerator .
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=
А
А
P (atm)
1
C
10
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process
B
50
-V (liters)
(a) Calculate the net work done by the gas.
kJ
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(c) Calculate the energy exhausted from the gas by heat.
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(d) Calculate the efficiency of the cycle.
%
80.0 L.
Chapter 20 Solutions
University Physics with Modern Physics Plus Mastering Physics with eText -- Access Card Package (14th Edition)
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