Question 1

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

Accepted Answer

The rms speed of a gas molecule depends only on the temperature of the gas, not on the pressure or volume. Therefore, the rms speed of the gas molecules will remain the same even if the pressure and volume change. The only factor that would change the rms speed is if the temperature changed, which is not indicated in the problem. Therefore, the answer is C) 2v, since the rms speed remains the same.

Question 2

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

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 3

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

Accepted Answer

According to the ideal gas law (PV = nRT), if pressure (P) and volume (V) are constant, the temperature (T) is directly proportional to the number of moles (n). Since container A has twice as many molecules as container B, T_A must be half of T_B to maintain the same pressure.

Question 4

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.)

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 5

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

Accepted Answer

The kinetic theory of gases states that the absolute temperature of an ideal gas is directly proportional to the average kinetic energy of its molecules. The other choices are not directly related to temperature. The average speed of the molecules and their momentum can vary independent of temperature, while the mass of the molecules only indirectly affects the temperature through its contribution to the average kinetic energy.

Question 6

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

Accepted Answer

The average molecular speed is inversely proportional to the square root of the mass. Since oxygen molecules are 16 times more massive than hydrogen molecules, their speed is 1/4 that of hydrogen molecules.

Question 7

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?

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 8

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?

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 multiplied by the square root of 2.

Question 9

When a gas expands adiabatically,

Accepted Answer

When a gas expands adiabatically, no heat is transferred between the system and the surroundings. Therefore, the internal (thermal) energy of the gas must decrease because it is doing work to expand against the external pressure. This work is coming from the internal energy of the gas, causing it to decrease.

Question 10

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.)

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 11

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

Accepted Answer

According to the first law of thermodynamics, for any system undergoing a process, the change in internal energy is given by ΔU = q + w, where q is the heat supplied to the system and w is the work done on the system. For an ideal gas, the internal energy depends only on its temperature, and so ΔU = C_vΔT, where C_v is the molar specific heat at constant volume and ΔT is the change in temperature. At constant pressure, the heat supplied to the system is used to increase both the internal energy and the work done by the gas, and so ΔU = q - PΔV = C_pΔT, where C_p is the molar specific heat at constant pressure and ΔV is the change in volume. Combining these equations, we get C_p = C_v + R, where R is the gas constant. Substituting C_v = 7R/2, we get C_p = 9R/2. Therefore, the answer is (D) 9R/2.

Question 12

For an ideal gas,

Accepted Answer

The answer of For an ideal gas,
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Question 13

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?

Accepted Answer

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

Question 14

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?

Accepted Answer

The root mean square (rms) speed of gas molecules is proportional to the square root of the absolute temperature. To double the rms speed, the temperature must be increased by a factor of 4, hence the new temperature should be 4T.

Question 15

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

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 16

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

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 17

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)

Accepted Answer

For an ideal gas, we know that 
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. 
R = 8.31 J/mol ∙ K 
Cp = 33.2 J/mol ∙ K 
Thus, 
Cv = Cp - R 
Cv = 33.2 J/mol ∙ K - 8.31 J/mol ∙ K = 24.9 J/mol ∙ K 
Therefore, the closest value of molar specific heat at constant volume is option D, which is 24.9 J/(mol*K).

Question 18

For an ideal gas,

Accepted Answer

For an ideal gas, $\frac { C _ { P } } { C _ { V } }$ (gamma) is always greater than 1 because $C_P$ is always greater than $C_V$ due to the additional work done at constant pressure.

Question 19

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,

Accepted Answer

At a given temperature, all gases have the same average kinetic energy. This is known as the Kinetic Theory of Gases. The mass of the molecule does not affect its average kinetic energy. Therefore, the average molecular kinetic energy of oxygen molecules is the same as that of hydrogen molecules.

Question 20

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?

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.

Quiz 12: Thermal Properties of Matter

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

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

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.)

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

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

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 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?

When a gas expands adiabatically,

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

For an ideal gas,

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?

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

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)

For an ideal gas,

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,

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?

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