University Physics with Modern Physics (14th Edition)
14th Edition
ISBN: 9780321973610
Author: Hugh D. Young, Roger A. Freedman
Publisher: PEARSON
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Textbook Question
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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(a) New-age power plants are often times forced to limit hot reservoir temperatures in steam engines to ~280 deg C due to the lack of sufficient heat-resistant materials. Assuming a reversible Carnot steam engine operating at this temperature uses room temperature (20 deg C) as the cold reservoir temperature, determine the total work produced by the system per complete cycle. The volumes for the system at each of the four Carnot states are V1 = 4.0 L, V2 = 16.0 L, V3 = 24.5 L, and V4 = 5.5 L. 1 mol of gas is used with a temperature-independent specific constant-volume heat capacity, CV = 1.9 kJ kg K . Assume the gas is carbon dioxide, with a molar mass of 44.01 g/mol.
(b) What is the efficiency, η, of this Carnot engine?
(c) What are three physical parameters that could be changed to improve the efficiency of the engine? Explain your answers.
The figure shows a reversible cycle through which 1.00 mole of a monatomic ideal gas is taken. Process bc is an adiabatic expansion, with pb = 5.80 atm and Vb = 1.00 x 10-3 m3. For the cycle, find (a) the energy added to the gas as heat, (b) the energy leaving the gas as heat, (c) the net work done by the gas, and (d) the efficiency of the cycle.
A certain gasoline engine is modeled as a monatomic ideal gas undergoing an Otto cycle, represented by the p-V diagram shown in the figure. The initial pressure, volume, and temperature are p1 = 1.05 × 105 Pa, V1 = 0.035 m3, and T1 = 290 K, respectively.
a)The first step in the Otto cycle is adiabatic compression. Enter an expression for the work performed on the gas during the first step, in terms of V1, V2, and p1.
b) Calculate the work performed on the gas during the first step, in joules, for V2 = V1/9.4.
c)Calculate the temperature of the gas, in kelvins, at the end of the first step.
Chapter 20 Solutions
University Physics with Modern Physics (14th Edition)
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