Question 1

An ideal gas is compressed isothermally to one-third of its initial volume. The resulting pressure will be
A)three times as large as the initial value.
B)less than three times as large as the initial value.
C)more than three times as large as the initial value.
D)equal to the initial value.
E)impossible to predict on the basis of this data.

Accepted Answer

For an ideal gas undergoing an isothermal process, the pressure-volume product (PV) remains constant (Boyle's Law). Therefore, if the volume is reduced to one-third of its initial value, the pressure must increase to three times its initial value to maintain the constant PV product.

Question 2

Two containers of equal volume each hold samples of the same ideal gas. Container A has twice as many molecules as container B. If the gas pressure is the same in the two containers, the correct statement regarding the absolute temperatures T_A and T_B in containers A and B, respectively, is A)T_A = T_B. B)T_A = 2T_B. C)T_A = $\frac { 1 } { 2 }$ T_B. D)T_A = $\frac { 1 } { \sqrt { 2 } }$ T_B. E)T_A = $\frac { 1 } { 4 }$ T_B.

Accepted Answer

According to the ideal gas law, PV = nRT. Since pressure and volume are the same for both containers, the ratio of temperatures is inversely proportional to the ratio of the number of molecules. Therefore, T_A = (1/2)T_B.

Question 3

For an ideal gas,
A) $\frac { C _ { P } } { C _ { V } }$ = 1 for all ideal gases.
B) $\frac { C _ { P } } { C _ { V } }$ < 1 for all monatomic and diatomic gases.
C) $\frac { C _ { P } } { C _ { V } }$ > 1 for all monatomic and diatomic gases.
D) $\frac { C _ { P } } { C _ { V } }$ < 1 only for a monatomic gas.
E) $\frac { C _ { P } } { C _ { V } }$ < 1 only for a diatomic gas.

Accepted Answer

For an ideal gas, the ratio $\frac { C _ { P } } { C _ { V } }$ is always greater than 1 because $C_P$ (heat capacity at constant pressure) is always greater than $C_V$ (heat capacity at constant volume).

Question 4

A certain ideal gas has a molar specific heat at constant volume 7R/2. What is its molar specific heat at constant pressure?
A)5R/2
B)3R/2
C)8R
D)9R/2
E)6R

Accepted Answer

The relationship between molar specific heats at constant volume and constant pressure is given by:
Cp - Cv = R
where Cp is the molar specific heat at constant pressure, Cv is the molar specific heat at constant volume, and R is the gas constant.

Substituting the given value of Cv = 7R/2, we get:
Cp - 7R/2 = R
Cp = 9R/2

Therefore, the molar specific heat at constant pressure is 9R/2, which is option D.

Question 5

An ideal gas is compressed isobarically to one-third of its initial volume. The resulting pressure will be
A)three times as large as the initial value.
B)equal to the initial value.
C)more than three times as large as the initial value.
D)impossible to predict on the basis of this data.

Accepted Answer

The pressure remains constant during an isobaric process, so compressing the gas to one-third of its initial volume does not change the pressure.

Question 6

A certain ideal gas has a molar specific heat at constant pressure of 33.2 J/mol ∙ K. Its molar specific heat at constant volume is closest to which of the following values? (R = 8.31J/mol ∙ K)
A)41.9 J/mol ∙ K
B)16.6 J/mol ∙ K
C)25.1 J/mol ∙ K
D)24.9 J/mol ∙ K
E)49.8 J/mol ∙ K

Accepted Answer

For an ideal gas, we know that $C_p - C_V = R$. Rearranging, we get $C_V = C_p - R$. Plugging in the given value for $C_p$, we get $C_V = 33.2~\mathrm{J/mol~K} - 8.31~\mathrm{J/mol~K} = 24.9~\mathrm{J/mol~K}$. The closest option is choice D.

Question 7

Oxygen molecules are 16 times more massive than hydrogen molecules. At a given temperature, the average molecular kinetic energy of oxygen molecules, compared to that of hydrogen molecules,
A)is greater.
B)is less.
C)is the same.
D)cannot be determined without knowing the pressure and volume.

Accepted Answer

The average molecular kinetic energy of a gas is directly proportional to its temperature and is independent of the mass of the molecules. Therefore, the kinetic energy of oxygen molecules and hydrogen molecules at a given temperature will be the same.

Question 8

The absolute temperature of a gas is T. In order to double the rms speed of its molecules, what should be the new absolute temperature?
A)4T
B)2T
C)T $\sqrt { 2 }$
D)8T
E)16T

Accepted Answer

The root mean square (rms) speed of gas molecules is proportional to the square root of the absolute temperature (v_rms ∝ √T). To double the rms speed, the temperature must be increased by a factor of 4 (since (2v_rms)^2 = 4v_rms^2), so the new temperature should be 4T.

Question 9

A mole of diatomic oxygen molecules and a mole of diatomic nitrogen molecules are at STP. Which statements are true about these molecules? (There could be more than one correct choice.)
A)Both gases have the same average molecular speeds.
B)Both gases have the same number of molecules.
C)Both gases have the same average kinetic energy per molecule.
D)Both gases have the same average momentum per molecule.

Accepted Answer

At STP (standard temperature and pressure), both gases have the same number of molecules because a mole of any substance contains Avogadro's number of entities (6.022 x 10^23). Additionally, the average kinetic energy per molecule for any ideal gas is dependent only on the temperature, according to the equation (3/2)kT, where k is the Boltzmann constant and T is the temperature in Kelvin. Since both gases are at the same temperature and pressure (STP), they have the same average kinetic energy per molecule. The average molecular speeds and average momentum per molecule will differ due to the different molecular masses of oxygen (O2) and nitrogen (N2).

Question 10

A sample of an ideal gas is heated and its Kelvin temperature doubles. If the root-mean-square speed of its molecules was originally v, what is the new root-mean-square speed?
A)4v
B)2v
C)v $\sqrt { 2 }$
D)v/ $\sqrt { 2 }$
E)v/4

Accepted Answer

The root-mean-square speed of gas molecules is proportional to the square root of the temperature in Kelvin. If the temperature doubles, the new speed is v√2.

Question 11

Oxygen molecules are 16 times more massive than hydrogen molecules. At a given temperature, how do their average molecular speeds compare? The oxygen molecules are moving
A)four times faster than the hydrogen molecules.
B)at 1/4 the speed of the hydrogen molecules.
C)sixteen times faster than the hydrogen molecules.
D)at 1/16 the speed of the hydrogen molecules.
E)at 1/ $\sqrt { 2 }$ the speed of the hydrogen molecules.

Accepted Answer

According to the kinetic theory of gases, the average speed of gas molecules is inversely proportional to the square root of their masses. Since oxygen molecules are 16 times more massive than hydrogen molecules, their average speed is 1/4 that of hydrogen molecules.

Question 12

A fixed container holds oxygen and helium gases at the same temperature. Which of the following statements are correct? (There could be more than one correct choice.)
A)The oxygen molecules have the greater average kinetic energy.
B)The helium molecules have the greater average kinetic energy.
C)The oxygen molecules have the greater speed.
D)The helium molecules have the greater speed.
E)The helium molecules have the same average kinetic as the oxygen molecules.

Accepted Answer

The average kinetic energy of gas molecules in a mixture at the same temperature is the same due to the equipartition theorem, making E correct. However, because helium atoms are lighter than oxygen molecules, they move faster at the same temperature, making D correct.

Question 13

The absolute temperature of an ideal gas is directly proportional to which of the following quantities?
A)the average speed of its molecules
B)the average momentum of its molecules
C)the average kinetic energy of its molecules
D)the mass of its molecules
E)It is proportional to all of the above quantities.

Accepted Answer

The kinetic theory of gases states that the average kinetic energy of gas molecules is directly proportional to the absolute temperature of the gas. This means that as the temperature of a gas increases, the average kinetic energy of its molecules increases proportionally. Therefore, the absolute temperature of an ideal gas is directly proportional to the average kinetic energy of its molecules, which is represented by choice C.

Question 14

Consider two equal-volume flasks of gas at the same temperature and pressure. One gas, oxygen, has a molecular mass of 32. The other gas, nitrogen, has a molecular mass of 28. What is the ratio of the number of oxygen molecules to the number of nitrogen molecules in these flasks?
A) $\frac { 32 } { 38 }$
B) $\frac { 28 } { 32 }$
C) $\sqrt { \frac { 28 } { 32 } }$
D) $\sqrt { \frac { 32 } { 28 } }$
E) $\frac { 1 } { 1 }$

Accepted Answer

According to Avogadro's law, equal volumes of gases at the same temperature and pressure contain the same number of molecules. Therefore, the ratio of the number of oxygen molecules to the number of nitrogen molecules is 1:1.

Question 15

The root-mean-square speed of the molecules of an ideal gas is v. The gas is now slowly compressed to one-half its original volume with no change in temperature. What is the root-mean-square speed of the molecules now?
A)4v
B)2v
C)v/ $\sqrt { 2 }$
D)v
E)v/2

Accepted Answer

The root-mean-square speed of gas molecules depends only on the temperature, not the volume. Since the temperature remains constant, the root-mean-square speed remains v.

Question 16

For an ideal gas, A)C_P = C_V for all ideal gases. B)C_P > C_V for all ideal gases. C)C_P < C_V for all ideal gases. D)it depends on whether the gas is monatomic or diatomic.

Accepted Answer

The answer of For an ideal gas, A)C_P = C_V for...

Question 17

An ideal gas is held in a container of volume V at pressure p. The rms speed of a gas molecule under these conditions is v. If now the volume and pressure are changed to 2V and 2p, the rms speed of a molecule will be
A)v/2
B)v
C)2v
D)4v
E)v/4

Accepted Answer

The rms speed is given by the equation v=sqrt(3kT/m), where k is the Boltzmann constant, T is the temperature, and m is the mass of a gas molecule. Since the gas is ideal, we know that the temperature is proportional to the pressure and inversely proportional to the volume, so T2/T1 = (2p)/(p) * (V/2V) = 1/2. Therefore, v2/v1 = sqrt(T2/T1) = sqrt(1/2) = 1/sqrt(2). Multiplying the original rms speed v by this factor gives v/sqrt(2), which can be simplified as v*sqrt(2)/2. Therefore, the answer is choice C) 2v.

Question 18

In a given reversible process, the temperature of an ideal gas is kept constant as the gas is compressed to a smaller volume. Which one of the following statements about the gas is correct?
A)The gas must absorb heat from its surroundings.
B)The gas must release heat to its surroundings.
C)The pressure of the gas also stays constant.
D)The process is adiabatic.
E)It is impossible to predict on the basis of this data.

Accepted Answer

As the temperature of the gas is kept constant during the compression process, the gas cannot absorb energy in the form of heat from its surroundings. Therefore, it must release energy in the form of heat to its surroundings. This energy release is necessary to maintain a constant temperature while the gas is being compressed. Choice A is incorrect for this reason. Choice C is also incorrect, as the pressure of the gas is increasing due to the compression process. Choice D is incorrect, as the process is not adiabatic if heat energy is being transferred between the gas and its surroundings. Choice E is not correct, as the information provided is sufficient to make a determination about the behavior of the gas during this process.

Question 19

A certain ideal gas has a molar specific heat at constant pressure of 7R/2. What is its molar specific heat at constant volume?
A)5R/2
B)3R/2
C)8R
D)9R/2
E)6R

Accepted Answer

The relationship between the molar specific heat at constant pressure (Cp) and the molar specific heat at constant volume (Cv) for an ideal gas is given by Cp - Cv = R. Given Cp = 7R/2, substituting into the equation gives 7R/2 - Cv = R, solving for Cv gives Cv = 5R/2.

Question 20

When a gas expands adiabatically,
A)the internal (thermal)energy of the gas decreases.
B)the internal (thermal)energy of the gas increases.
C)it does no work.
D)work is done on the gas.
E)the temperature of the gas remains constant.

Accepted Answer

Adiabatic expansion means no heat is exchanged with the surroundings, so any decrease in internal energy must be due to work done by the expanding gas. This work comes at the expense of the internal energy, causing a decrease.

Quiz 12: Thermal Properties of Matter

An ideal gas is compressed isothermally to one-third of its initial volume. The resulting pressure will be

Two containers of equal volume each hold samples of the same ideal gas. Container A has twice as many molecules as container B. If the gas pressure is the same in the two containers, the correct statement regarding the absolute temperatures TA and TB in containers A and B, respectively, is

For an ideal gas,

A certain ideal gas has a molar specific heat at constant volume 7R/2. What is its molar specific heat at constant pressure?

An ideal gas is compressed isobarically to one-third of its initial volume. The resulting pressure will be

A certain ideal gas has a molar specific heat at constant pressure of 33.2 J/mol ∙ K. Its molar specific heat at constant volume is closest to which of the following values? (R = 8.31J/mol ∙ K)

Oxygen molecules are 16 times more massive than hydrogen molecules. At a given temperature, the average molecular kinetic energy of oxygen molecules, compared to that of hydrogen molecules,

The absolute temperature of a gas is T. In order to double the rms speed of its molecules, what should be the new absolute temperature?

A mole of diatomic oxygen molecules and a mole of diatomic nitrogen molecules are at STP. Which statements are true about these molecules? (There could be more than one correct choice.)

A sample of an ideal gas is heated and its Kelvin temperature doubles. If the root-mean-square speed of its molecules was originally v, what is the new root-mean-square speed?

Oxygen molecules are 16 times more massive than hydrogen molecules. At a given temperature, how do their average molecular speeds compare? The oxygen molecules are moving

A fixed container holds oxygen and helium gases at the same temperature. Which of the following statements are correct? (There could be more than one correct choice.)

The absolute temperature of an ideal gas is directly proportional to which of the following quantities?

Consider two equal-volume flasks of gas at the same temperature and pressure. One gas, oxygen, has a molecular mass of 32. The other gas, nitrogen, has a molecular mass of 28. What is the ratio of the number of oxygen molecules to the number of nitrogen molecules in these flasks?

The root-mean-square speed of the molecules of an ideal gas is v. The gas is now slowly compressed to one-half its original volume with no change in temperature. What is the root-mean-square speed of the molecules now?

For an ideal gas,

An ideal gas is held in a container of volume V at pressure p. The rms speed of a gas molecule under these conditions is v. If now the volume and pressure are changed to 2V and 2p, the rms speed of a molecule will be

In a given reversible process, the temperature of an ideal gas is kept constant as the gas is compressed to a smaller volume. Which one of the following statements about the gas is correct?

A certain ideal gas has a molar specific heat at constant pressure of 7R/2. What is its molar specific heat at constant volume?

When a gas expands adiabatically,

Two containers of equal volume each hold samples of the same ideal gas. Container A has twice as many molecules as container B. If the gas pressure is the same in the two containers, the correct statement regarding the absolute temperatures T_A and T_B in containers A and B, respectively, is