Physics

Multiple Choice

How much heat energy is needed to increase the temperature of 5 mol of an ideal diatomic gas by from 273K to 300K if the a) pressure is held constant; b) the volume is held constant?

CALC The temperature of 0.150 mol of an ideal gas is held constant at 77.0°C while its volume is reduced to 25.0% of its initial volume. The initial pressure of the gas is 1.25 atm. (c) Does the gas exchange heat with its surroundings? If so, how much? Does the gas absorb or liberate heat?

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Textbook Question

A cylinder contains 0.100 mol of an ideal monatomic gas. Initially the gas is at 1.00 * 10^5 Pa and occupies a volume of 2.50 * 10^-3 m^3. (b) If the gas is allowed to expand to twice the initial volume, find the final temperature (in kelvins) and pressure of the gas if the expansion is (i) isothermal; (ii) isobaric; (iii) adiabatic.

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Textbook Question

A cylinder contains 0.100 mol of an ideal monatomic gas. Initially the gas is at 1.00 * 10^5 Pa and occupies a volume of 2.50 * 10^-3 m^3. (b) If the gas is allowed to expand to twice the initial volume, find the final temperature (in kelvins) and pressure of the gas if the expansion is (i) isothermal; (ii) isobaric; (iii) adiabatic.

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Textbook Question

A cylinder contains 0.100 mol of an ideal monatomic gas. Initially the gas is at 1.00 * 10^5 Pa and occupies a volume of 2.50 * 10^-3 m^3. (b) If the gas is allowed to expand to twice the initial volume, find the final temperature (in kelvins) and pressure of the gas if the expansion is (i) isothermal; (ii) isobaric; (iii) adiabatic.

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Textbook Question

On a warm summer day, a large mass of air (atmospheric pressure 1.01 * 10^5 Pa) is heated by the ground to 26.0°C and then begins to rise through the cooler surrounding air. (This can be treated approximately as an adiabatic process; why?) Calculate the temperature of the air mass when it has risen to a level at which atmospheric pressure is only 0.850 * 105 Pa. Assume that air is an ideal gas, with g = 1.40. (This rate of cooling for dry, rising air, corresponding to roughly 1 C° per 100 m of altitude, is called the dry adiabatic lapse rate.)

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Textbook Question

A player bounces a basketball on the floor, compressing it to 80.0% of its original volume. The air (assume it is essentially N2 gas) inside the ball is originally at 20.0°C and 2.00 atm. The ball's inside diameter is 23.9 cm. (a) What temperature does the air in the ball reach at its maximum compression? Assume the compression is adiabatic and treat the gas as ideal.

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Textbook Question

The engine of a Ferrari F355 F1 sports car takes in air at 20.0°C and 1.00 atm and compresses it adiabatically to 0.0900 times the original volume. The air may be treated as an ideal gas with g = 1.40. (b) Find the final temperature and pressure.

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Textbook Question

A monatomic ideal gas that is initially at 1.50 * 10^5 Pa and has a volume of 0.0800 m^3 is compressed adiabatically to a volume of 0.0400 m^3. (c) What is the ratio of the final temperature of the gas to its initial temperature? Is the gas heated or cooled by this compression?

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Textbook Question

A monatomic ideal gas that is initially at 1.50 * 10^5 Pa and has a volume of 0.0800 m^3 is compressed adiabatically to a volume of 0.0400 m^3. (a) What is the final pressure?

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Textbook Question

Five moles of monatomic ideal gas have initial pressure 2.50 * 10^3 Pa and initial volume 2.10 m^3 . While undergoing an adiabatic expansion, the gas does 1480 J of work. What is the final pressure of the gas after the expansion?

During an isothermal compression of an ideal gas, 410 J of heat must be removed from the gas to maintain constant temperature. How much work is done by the gas during the process?

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Textbook Question

5.0 g of nitrogen gas at 20°C and an initial pressure of 3.0 atm undergo an isobaric expansion until the volume has tripled. a. What are the gas volume and temperature after the expansion?

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Textbook Question

5.0 g of nitrogen gas at 20°C and an initial pressure of 3.0 atm undergo an isobaric expansion until the volume has tripled. b. How much heat energy is transferred to the gas to cause this expansion?

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Textbook Question

5.0 g of nitrogen gas at 20°C and an initial pressure of 3.0 atm undergo an isobaric expansion until the volume has tripled. c. What is the gas pressure after the decrease?

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Textbook Question

5.0 g of nitrogen gas at 20°C and an initial pressure of 3.0 atm undergo an isobaric expansion until the volume has tripled. d. What amount of heat energy is transferred from the gas as its pressure decreases?

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Textbook Question

FIGURE CP19.80 shows a thermodynamic process followed by 0.015 mol of hydrogen. How much heat energy is transferred to the gas?

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Textbook Question

An ideal-gas process is described by p=cV^ /2, where c is a constant. a.Find an expression for the work done on the gas in this process as the volume changes from V₁ to V₂.

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Textbook Question

n moles of an ideal gas at temperature T1 and volume V1 expand isothermally until the volume has doubled. In terms of n, T₁ , and V₁, what are (a) the final temperature,

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Textbook Question

n moles of an ideal gas at temperature T1 and volume V1 expand isothermally until the volume has doubled. In terms of n, T₁ , and V₁, what are (b) the work done on the gas, and

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Textbook Question

n moles of an ideal gas at temperature T1 and volume V1 expand isothermally until the volume has doubled. In terms of n, T₁ , and V₁, what are (c) the heat energy transferred to the gas?

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Textbook Question

An ideal-gas process is described by p=cV^ /2, where c is a constant. b. 0.033 mol of gas at an initial temperature of 150°C is compressed, using this process, from 300 cm^3 to 200 cm^3. How much work is done on the gas?

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Textbook Question

n₁ moles of a monatomic gas and n₂ moles of a diatomic gas are mixed together in a container. a. Derive an expression for the molar specific heat at constant volume of the mixture.

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Textbook Question

(II) The pressure in an ideal gas is cut in half slowly, while being kept in a container with rigid walls. In the process, 425 kJ of heat left the gas.

(a) How much work was done during this process?

(b) What was the change in internal energy of the gas during this process?

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Textbook Question

An audience of 1600 fills a concert hall of volume 22, 000 m³. If there were no ventilation, by how much would the temperature of the air rise over a period of 2.0 h due to the metabolism of the people (70 W/person)?

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Textbook Question

(II) A 2.00-mole sample of N₂ gas at 0°C is heated to 150°C at constant pressure (1.00 atm). Determine (a) the change in internal energy, (b) the work the gas does, and (c) the heat added to it.

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Textbook Question

(II) Show that the work done by n moles of an ideal gas when it expands adiabatically is W = nC_v( T₁ - T₂) , where T₁ and T₂ are the initial and final temperatures, and C_v is the molar specific heat at constant volume.

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Textbook Question

A bicycle pump is a cylinder 22 cm long and 3.0 cm in diameter. The pump contains air at 20.0°C and 1.0 atm. If the outlet at the base of the pump is blocked and the handle is pushed in very quickly, compressing the air to half its original volume, how hot does the air in the pump become?

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Textbook Question

(II) Show, using Eqs. 19–7 and 19–16, that the work done by a gas that slowly expands adiabatically from pressure P₁ and volume V₁ , to P₂ and V₂, is given by W = (P₁V₁ - P₂V₂) / (γ - 1).

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Textbook Question

(II) Consider the following two-step process. Heat is allowed to flow out of an ideal gas at constant volume so that its pressure drops from 2.2 atm to 1.4 atm. Then the gas expands at constant pressure, from a volume of 5.9 L to 9.3 L, where the temperature reaches its original value. Calculate

(a) the total work done by the gas in the process,

(b) the change in internal energy of the gas in the process, and

(c) the total heat flow into or out of the gas.

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Textbook Question

At very low temperatures, the molar specific heat of many substances varies as the cube of the absolute temperature:

C = k (T³ / T³₀)

which is sometimes called Debye’s law. For rock salt, T₀ = 281 K and k = 1940 J/mol · K. Determine the heat needed to raise 2.75 mol of salt from 22.0 K to 46.0 K.

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Textbook Question

Suppose 3.0 mol of neon (a monatomic gas, assume ideal) at STP are compressed slowly and isothermally to 0.22 the original volume. The gas is then allowed to expand quickly and adiabatically back to its original volume. Find the highest and lowest temperatures and pressures attained by the gas, and show on a PV diagram where these values occur.

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Textbook Question

The beaker in FIGURE P19.45, with a thin metal bottom, is filled with 20 g of water at 20°C. It is brought into good thermal contact with a 4000 cm^3 container holding 0.40 mol of a monatomic gas at 10 atm pressure. Both containers are well insulated from their surroundings. What is the gas pressure after a long time has elapsed? You can assume that the containers themselves are nearly massless and do not affect the outcome.

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Textbook Question

A 100 cm³ box contains helium at a pressure of 2.0 atm and a temperature of 100℃. It is placed in thermal contact with a 200 cm³ box containing argon at a pressure of 4.0 atm and a temperature of 400℃. c. How much heat energy is transferred, and in which direction?

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Textbook Question

Propane gas (C3H8) behaves like an ideal gas with g = 1.127. Determine the molar heat capacity at constant volume and the molar heat capacity at constant pressure

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Textbook Question

An experimenter adds 970 J of heat to 1.75 mol of an ideal gas to heat it from 10.0°C to 25.0°C at constant pressure. The gas does +223 J of work during the expansion. (b) Calculate γ for the gas.

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Textbook Question

Heat Q flows into a monatomic ideal gas, and the volume increases while the pressure is kept constant. What fraction of the heat energy is used to do the expansion work of the gas?

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Textbook Question

0.10 mol of nitrogen gas follow the two processes shown in FIGURE P19.58. How much heat is required for each?

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Textbook Question

One cylinder in the diesel engine of a truck has an initial volume of 600 cm^3. Air is admitted to the cylinder at 30°C and a pressure of 1.0 atm. The piston rod then does 400 J of work to rapidly compress the air. What are its final temperature and volume?

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Textbook Question

A gas cylinder holds 0.10 mol of O₂ at 150°C and a pressure of 3.0 atm. The gas expands adiabatically until the volume is doubled. What are the final (a) pressure and

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Textbook Question

A gas cylinder holds 0.10 mol of O₂ at 150°C and a pressure of 3.0 atm. The gas expands adiabatically until the pressure is halved. What are the final (b) temperature?

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Textbook Question

The volume of a gas is halved during an adiabatic compression that increases the pressure by a factor of 2.5. a. What is the specific heat ratio γ?

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Textbook Question

14 g of nitrogen gas at STP are adiabatically compressed to a pressure of 20 atm. What are (d) the compression ratio Vₘₐₓ/Vₘᵢₙ?

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Textbook Question

A monatomic gas is adiabatically compressed to ⅛ of its initial volume. Does each of the following quantities change? If so, does it increase or decrease, and by what factor? If not, why not? c. The thermal energy of the gas.

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Textbook Question

A monatomic gas is adiabatically compressed to ⅛ of its initial volume. Does each of the following quantities change? If so, does it increase or decrease, and by what factor? If not, why not? d. The molar specific heat at constant volume.

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Textbook Question

A cylinder contains 0.0100 mol of helium at T = 27.0°C. (a) How much heat is needed to raise the temperature to 67.0°C while keeping the volume constant? Draw a pV-diagram for this process. (b) If instead the pressure of the helium is kept constant, how much heat is needed to raise the temperature from 27.0°C to 67.0°C? Draw a pV-diagram for this process. (c) What accounts for the difference between your answers to parts (a) and (b)? In which case is more heat required? What becomes of the additional heat? (d) If the gas is ideal, what is the change in its internal energy in part (a)? In part (b)? How do the two answers compare? Why?

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Textbook Question

A cylinder contains 0.0100 mol of helium at T = 27.0°C. (a) How much heat is needed to raise the temperature to 67.0°C while keeping the volume constant? Draw a pV-diagram for this process. (b) If instead the pressure of the helium is kept constant, how much heat is needed to raise the temperature from 27.0°C to 67.0°C? Draw a pV-diagram for this process. (c) What accounts for the difference between your answers to parts (a) and (b)? In which case is more heat required? What becomes of the additional heat? (d) If the gas is ideal, what is the change in its internal energy in part (a)? In part (b)? How do the two answers compare? Why?

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Textbook Question

A cylinder contains 0.0100 mol of helium at T = 27.0°C. (a) How much heat is needed to raise the temperature to 67.0°C while keeping the volume constant? Draw a pV-diagram for this process. (b) If instead the pressure of the helium is kept constant, how much heat is needed to raise the temperature from 27.0°C to 67.0°C? Draw a pV-diagram for this process. (c) What accounts for the difference between your answers to parts (a) and (b)? In which case is more heat required? What becomes of the additional heat? (d) If the gas is ideal, what is the change in its internal energy in part (a)? In part (b)? How do the two answers compare? Why?

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Textbook Question

A cylinder contains 0.0100 mol of helium at T = 27.0°C. (a) How much heat is needed to raise the temperature to 67.0°C while keeping the volume constant? Draw a pV-diagram for this process. (b) If instead the pressure of the helium is kept constant, how much heat is needed to raise the temperature from 27.0°C to 67.0°C? Draw a pV-diagram for this process. (c) What accounts for the difference between your answers to parts (a) and (b)? In which case is more heat required? What becomes of the additional heat? (d) If the gas is ideal, what is the change in its internal energy in part (a)? In part (b)? How do the two answers compare? Why?

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Textbook Question

(II) A 1.00-mol sample of an ideal diatomic gas, originally at 1.00 atm and 20°C, expands adiabatically to 1.75 times its initial volume. What are the final pressure and temperature for the gas? (Assume no molecular vibration.)

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