(a)
The initial volume of the air in the pump.
(a)
Answer to Problem 32P
The initial volume of the air in the pump is
Explanation of Solution
Write the expression for volume of the cylinder.
Here,
Rewrite the above equation.
Here,
Conclusion:
Substitute
Therefore, the initial volume of the air in the pump is
(b)
The number of moles of air in the pump.
(b)
Answer to Problem 32P
The number of moles of air in the pump is
Explanation of Solution
Write the expression from
Here,
Conclusion:
Substitute
Therefore, the number of moles of air in the pump is
(c)
The absolute pressure of the compressed air.
(c)
Answer to Problem 32P
The absolute pressure of the compressed air is
Explanation of Solution
Write the expression for absolute pressure.
Here,
Conclusion:
Substitute
Therefore, the absolute pressure of the compressed air is
(d)
The volume of the compressed air.
(d)
Answer to Problem 32P
The volume of the compressed air is
Explanation of Solution
Write the expression from an adiabatic compression process.
Here,
Rearrange the above expression for
Conclusion:
Substitute
Therefore, the volume of the compressed air is
(e)
The temperature of the compressed air.
(e)
Answer to Problem 32P
The temperature of the compressed air is
Explanation of Solution
Write the expression from an adiabatic compression process to find final temperature.
Here,
Rewrite the above expression.
Conclusion:
Substitute
Therefore, the temperature of the compressed air is
(f)
The increasing internal energy of the gas.
(f)
Answer to Problem 32P
The increasing internal energy of the gas is
Explanation of Solution
Write the expression for internal energy of the any gas.
Here,
The specific heat capacity at constant volume for diatomic gas is,
Conclusion:
Substitute equation (VII) in equation (VI).
Substitute
Therefore, the increasing internal energy of the gas is
(g)
The volume of the steel in this
(g)
Answer to Problem 32P
The volume of the steel in this
Explanation of Solution
Write the expression for volume of the steel.
Here,
Conclusion:
Substitute
Therefore, the volume of the steel in this
(h)
The mass of the steel.
(h)
Answer to Problem 32P
The mass of the steel is
Explanation of Solution
Write the expression for mass of the steel.
Here,
Conclusion:
Substitute
Therefore, the mass of the steel is
(i)
The increasing temperature of the steel.
(i)
Answer to Problem 32P
The increasing temperature of the steel is
Explanation of Solution
Write the expression for temperature of the steel.
Here,
Rewrite the above expression.
Conclusion:
Substitute
Therefore, the increasing temperature of the steel is
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Chapter 21 Solutions
Physics for Scientists and Engineers with Modern Physics Technology Update
- When a gas undergoes an adiabatic expansion, which of the following statements is true? (a) The temperature of the gas does not change. (b) No work is done by the gas. (c) No energy is transferred to the gas by heat. (d) The internal energy of the gas does not change. (e) The pressure increases.arrow_forwardDuring the power stroke in a four-stroke automobile engine, the piston is forced down as the mixture of combustion products and air undergoes an adiabatic expansion. Assume (1) the engine is running at 2 500 cycles/min; (2) the gauge pressure immediately before the expansion is 20.0 atm; (3) the volumes of the mixture immediately before and after the expansion are 50.0 cm3 and 400 cm3, respectively (Fig. P21.31); (4) the time interval for the expansion is one-fourth that of the total cycle; and (5) the mixture behaves like an ideal gas with specific heat ratio 1.40. Find the average power generated during the power stroke.arrow_forwardIf a gas is compressed isothermally, which of the following statements is true? (a) Energy is transferred into the gas by heat. (b) No work is done on the gas. (c) The temperature of the gas increases. (d) The internal energy of the gas remains constant. (e) None of those statements is true.arrow_forward
- One mole of an ideal gas does 3 000 J of work on its surroundings as it expands isothermally to a final pressure of 1.00 atm and volume of 25.0 L. Determine (a) the initial volume and (b) the temperature of the gas.arrow_forwardAn ideal gas initially at 300 K undergoes an isobaric expansion at 2.50 kPa. If the volume increases from 1.00 m3 to 3.00 m3 and 12.5 kJ is transferred to the gas by heat, what are (a) the change in its internal energy and (b) its final temperature?arrow_forwardThe arrow OA in the PV diagram shown in Figure OQ22.11 represents a reversible adiabatic expansion of an ideal gas. The same sample of gas, starting from the same state O. now undergoes an adiabatic free expansion to the same final volume. What point on the diagram could represent the final state of the gas? (a) the same point A as for the reversible expansion (b) point B (c) point C (d) any of those choices (e) none of those choicesarrow_forward
- A sample of a monatomic ideal gas occupies 5.00 L at atmospheric pressure and 300 K (point A in Fig. P17.68). It is warmed at constant volume to 3.00 atm (point B). Then it is allowed to expand isothermally to 1.00 atm (point C) and at last compressed isobarically to its original state. (a) Find the number of moles in the sample. Find (b) the temperature at point B, (c) the temperature at point C, and (d) the volume at point C. (e) Now consider the processes A B, B C, and C A. Describe how to carry out each process experimentally. (f) Find Q, W, and Eint for each of the processes. (g) For the whole cycle A B C A, find Q, W, and Eint. Figure P17.68arrow_forwardA monatomic ideal gas undergoes a quasi-static adiabatic expansion in which its volume is doubled. How is the pressure of the gas changed?arrow_forwardYou have a particular interest in automobile engines, so you have secured a co-op position at an automobile company while you attend school. Your supervisor is helping you to learn about the operation of an internal combustion engine. She gives you the following assignment, related to a simulation of a new engine she is designing. A gas, beginning at PA = 1.00 atm, VA = 0.500 L, and TA = 27.0C, is compressed from point A on the PV diagram in Figure P19.31 (page 530) to point B. This represents the compression stroke in a fourcycle gasoline engine. At that point, 132 J of energy is delivered to the gas at constant volume, taking the gas to point C. This represents the transformation of potential energy in the gasoline to internal energy when the spark plug fires. Your supervisor tells you that the internal energy of a gas is proportional to temperature (as we shall find in Chapter 20), the internal energy of the gas at point A is 200 J, and she wants to know what the temperature of the gas is at point C. Figure P19.31arrow_forward
- A multicylinder gasoline engine in an airplane, operating at 2.50 103 rev/min, takes in energy 7.89 103 J and exhausts 4.58 103 J for each revolution of the crankshaft. (a) How many liters of fuel does it consume in 1.00 h of operation if the heat of combustion of the fuel is equal to 4.03 107 J/L? (b) What is the mechanical power output of the engine? Ignore friction and express the answer in horsepower. (c) What is the torque exerted by the crankshaft on the load? (d) What power must the exhaust and cooling system transfer out of the engine?arrow_forward(a) Determine the work done on a gas that expands from i to f as indicated in Figure P19.16. (b) What If? How much work is done on the gas if it is compressed from f to i along the same path? Figure P19.16arrow_forward
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