PHYSICS F/SCI.+ENGRS.,STAND.-W/ACCESS
6th Edition
ISBN: 9781429206099
Author: Tipler
Publisher: MAC HIGHER
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Chapter 19, Problem 32P
To determine
The efficiency of the cycle.
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A 2.00-mol sample of a diatomic ideal gas expands slowly and adiabatically from a pressure of 4.90 atm and a volume of 12.2 L to a final volume of 29.4 L.
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Expansion of an ideal gas. An ideal gas sample contains n moles, initially has a volume Viand a temperature Ti, and at the end of the expansion has a volume Vf > Vi. We will study threeprocesses. Process I is an adiabatic expansion against vacuum: the gas initially is contained in one partof an insulated container, with the other part being empty, and the partition separating the two parts issuddenly removed, allowing the gas to expand against zero pressure. Process II is a reversible isothermalexpansion. Process III is a reversible adiabatic expansion. For each of the three processes, determine theheat Q absorbed by the gas, the work W done on the gas, and the changes ∆E, ∆T and ∆S in the energy,temperature and entropy. Write all results in terms of n, R, Vi, Vf , and Ti. Compare the results for thethree processes, and indicate which quantities are the same for each pair of processes (I and II; II and III;I and III), or what is the direction of their inequality if they are…
The volume of 1 mol of an ideal gas initially at 2 atm, 25 oC and 12.2 L volume is doubled by an reversible expansion along a path P = aV+b, where P is in atm, V in Land a and b are constants. Calculate the work done during this process if constant a = 0.1 atm L- 1.
Chapter 19 Solutions
PHYSICS F/SCI.+ENGRS.,STAND.-W/ACCESS
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- Two moles of a monatomic ideal gas such as oxygen is compressed adiabatically and reversibly from a state (3 atm, 5 L) to a state with a pressure of 4 atm. (a) Find the volume and temperature of the final state. (b) Find the temperature of the initial state. (c) Find work done by the gas in the process. (d) Find the change in internal energy in the process. Assume Cv=5R and Cp=Cv+R for the diatomic ideal gas in the conditions given.arrow_forwardIn an adiabatic process, oxygen gas in a container is compressed along a path that can be described by the following pressure in atm as a function of volume V, with V0=1L:P=(3.0atm)(V/V)1.2 . The initial and final volumes during the process were 2 L and 1.5 L, respectively. Find the amount of work done on the gas.arrow_forwardA car tile contains 0.0380 m3 of air at a pressure of 2.20105 Pa (about 32 psi). How much more internal energy does this gas have than the same volume has at zero gauge pressure (which is equivalent to normal atmospheric pressure)?arrow_forward
- An ideal gas has a pressure of 0.50 atm and a volume of 10 L. It is compressed adiabatically and quasi-statically until its pressure is 3.0 atm and its volume is 2.8 L. Is the monatomic, diatomic, or polyatomic?arrow_forwardTwo moles of nitrogen gas, with =7/5 for ideal diatomic gases, occupies a volume of 102 m3 in an insulated cylinder at temperature 300 K. The gas is adiabatically and reversibly compressed to a volume of 5 L. The piston of the cylinder is locked in its place, and the insulation around the cylinder is removed. The heat-conducting cylinder is then placed in a 300-K bath. Heat from the compressed gas leaves the gas, and the temperature of the gas becomes 300 K again. The gas is then slowly expanded at the fixed temperature 300 K until the volume of the gas becomes 102 m3, thus making a complete cycle for the gas. For the entire cycle, calculate (a) the work done by the gas, (b) the heat into or out of the gas, (c) the change in the internal energy of the gas, and (d) the change in entropy of the gas.arrow_forwardIn a diesel engine, the fuel is ignited without a spark plug. Instead, air in a cylinder is compressed adiabatically to a temperature above the ignition temperature of the fuel; at the point of maximum compression, the fuel is injected into the cylinder. Suppose that air at 20 C is taken into the cylinder at a volume V1 and then compressed adiabatically and quasi-statically to a temperature of 600 C and a volume V2 . If =1.4 , what is the ratio V1/V2 ? (Note: static. In an operating diesel engine, the compression is not quasi-arrow_forward
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- A Carnot engine employs 1.5 mol of nitrogen gas as a working substance, which is considered as an ideal diatomic gas with =7.5 at the working temperatures of the engine. The Carnot cycle goes in the cycle ABCDA with AB being an isothermal expansion. The volume at points A and C of the cycle are 5.0103 m3 and 0.15 L, respectively. The engine operates between two thermal baths of temperature 500 K 300 K. (a) Find the values of volume at B and D. (b) How much heat is absorbed by the gas in the AB isothermal expansion? (c) How much work is done by the gas in the AB isothermal expansion? (d) How much heat is given up by the gas in the CD isothermal expansion? (e) How much work is done by the gas in the CD isothermal compression? (f) How much work is done by the gas in the BC adiabatic expansion? (g) How much work is done by the gas in the DA adiabatic compression? (h) Find the value of efficiency of the engine based on the net and heat input. Compare this value to the efficiency of a Carnot engine based on the temperatures of the baths.arrow_forwardAn amount of n moles of a monatomic ideal gas in a conducting container with a movable piston is placed in a large thermal heat bath at temperature T1 and the gas is allowed to come to equilibrium. After the equilibrium is leached, the pressure on the piston is lowered so that the gas expands at constant temperature. The process is continued quasi-statically until the final pressure is 4/3 of the initial pressure p1 . (a) Find the change in the internal energy of the gas. (b) Find the work done by the gas. (c) Find the heat exchanged by the gas, and indicate, whether the gas takes in or gives up heat.arrow_forwardWhen 400 J of heat are slowly added to 10 mol of an ideal monatomic gas, its temperature rises by 10 . What is the work done on the gas?arrow_forward
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