Question 1

Which two temperature changes are equivalent?

Accepted Answer

1°C and 1 K are equivalent temperature changes because they have the same magnitude. However, 1 K is larger than 1°C on an absolute temperature scale, such as the Kelvin scale. Option A is incorrect because 1 K is not equal to 1°F, and option B is incorrect because 1°F and 1°C do not have the same magnitude.

Question 2

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 the molecules in an ideal gas depends only on the temperature of the gas, not on its volume. Since the temperature remains unchanged, the root-mean-square speed remains the same, v.

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. Since the pressure and volume are the same for both containers, and container A has twice as many molecules (n) as container B, the temperature in container A must be half that of container B to maintain the same pressure. Thus, T_A = $\frac { 1 } { 2 }$ T_B.

Question 4

When a heavy metal block is supported by a cylindrical vertical post of radius R,it exerts a force F on the post.If the diameter of the post is increased to 2R,what force does the block now exert on the post?

Accepted Answer

The force exerted by the block on the post is determined by its weight, which does not change with the change in the post's diameter. Therefore, the force remains the same, F.

Question 5

A compressed gas with a total mass of $107 \mathrm {~kg}$ is stored in a spherical container having a radius of 0.521 m.What is the density of the compressed gas?

Accepted Answer

The volume V of a sphere with radius r is given by the formula:

$$V = \frac{4}{3}\pi r^3$$

Substituting the given radius, we get:

$$V = \frac{4}{3}\pi (0.521 \mathrm{~m})^3 = 0.603 \mathrm{~m^3}$$

The density of the compressed gas can be found using the formula:

$$\rho = \frac{m}{V}$$

Substituting the given mass and calculated volume, we get:

$$\rho = \frac{107 \mathrm{~kg}}{0.603 \mathrm{~m^3}} \approx 177 \mathrm{~kg/m^3}$$

Therefore, the closest answer choice to our calculated density is A) 181 kg/m3.

Question 6

When a box rests on a round sheet of wood on the ground,it exerts an average pressure p on the wood.If the wood is replaced by a sheet that has half the diameter of the original piece,what is the new average pressure?

Accepted Answer

Pressure is defined as force per unit area. When the diameter of the wood sheet is halved, its area becomes one-fourth of the original (since area of a circle is proportional to the square of its diameter). Given the same force (weight of the box), the pressure quadruples.

Question 7

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, regardless of their molecular masses.

Question 8

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 is given by the equation:

v = √(3kT/m)

Where k is the Boltzmann constant, T is the temperature, and m is the mass of the gas molecule.

Since the gas is ideal, we can use the ideal gas law:

PV = nRT

Where n is the number of moles of gas and R is the gas constant.

We can rearrange this equation to solve for T:

T = PV/nR

Plugging this into the equation for v, we get:

v = √(3kPV/mnR)

Now, when the volume and pressure are changed to 2V and 2p, the temperature remains constant (since the gas is not heated or cooled). Therefore, we can use the same equation for v, but with the new values of pressure and volume:

v' = √(3k(2p)(2V)/mnR)

Simplifying this expression, we get:

v' = √(3kPV/mnR) x √2

Or, v' = v x √2

Therefore, the rms speed of a molecule will be √2 times the original rms speed, or (approximately) 1.41 times the original speed. The closest answer choice is C, 2v.

Question 9

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 directly proportional to the square root of the absolute temperature (T). Therefore, to double the rms speed, the temperature must be quadrupled (since $2^2 = 4$).

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?

Accepted Answer

The root-mean-square speed of molecules in an ideal gas is directly proportional to the square root of the temperature in Kelvin. If the temperature doubles, the new speed is $v \sqrt{2}$.

Question 11

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

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

Question 12

A styrofoam sphere of radius R has a density ρ.You now carefully compress the sphere so its radius is R/2.What is the density of the compressed sphere?

Accepted Answer

The density of an object is given by its mass divided by its volume. When the radius of the sphere is halved, its volume decreases by a factor of $ \left(\frac{1}{2}\right)^3 = \frac{1}{8} $. Since the mass remains constant but the volume decreases to 1/8th of its original volume, the density increases by a factor of 8, making the new density $8 \rho$.

Question 13

The temperature in your classroom is closest to

Accepted Answer

We can assume that the temperature in the classroom is in degrees Celsius since that is the most common unit used to measure temperature in everyday situations. However, the most common unit used in science is Kelvin. Therefore, we need to convert Celsius to Kelvin using the formula K = °C + 273.15. 
Assuming the temperature is 22°C (a comfortable room temperature), we have:
K = 22°C + 273.15 = 295.15 K
Therefore, the closest temperature is 295 K, which corresponds to answer choice D.

Question 14

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 15

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 molecules (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, they have the same average kinetic energy per molecule. The average molecular speeds and average momentum per molecule differ due to the difference in molecular masses of oxygen (O2) and nitrogen (N2).

Question 16

A plastic block of dimensions 2.00 cm × 3.00 cm × 4.00 cm has a mass of 30.0 g.What is its density?

Accepted Answer

Density is defined as mass per unit volume. In this case, we have a mass of 30.0 g and a volume of (2.00 cm)*(3.00 cm)*(4.00 cm) = 24.00 cm^3. Dividing the mass by the volume, we get a density of 30.0 g/24.00 cm^3 = 1.25 g/cm^3. Therefore, the correct answer is choice C.

Question 17

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

Accepted Answer

The average kinetic energy of its molecules is directly proportional to the absolute temperature of an ideal gas, according to the kinetic theory of gases. This means that as temperature increases, the average kinetic energy of the molecules will also increase. The other choices (A, B, and D) are not directly proportional to temperature but may have some relationship to it.

Question 18

A hollow sphere of negligible mass and radius R is completely filled with a liquid so that its density is ρ.You now enlarge the sphere so its radius is 2R and completely fill it with the same liquid.What is the density of the enlarged sphere?

Accepted Answer

The mass of the initial sphere can be calculated as:

$M_1 = \frac{4}{3} \pi R^3 \rho$

The mass of the final sphere can be calculated as:

$M_2 = \frac{4}{3} \pi (2R)^3 \rho = \frac{32}{3} \pi R^3 \rho$

The volume of the liquid in the initial sphere is:

$V_1 = \frac{4}{3} \pi R^3$

The volume of the liquid in the final sphere is:

$V_2 = \frac{4}{3} \pi (2R)^3 - \frac{4}{3} \pi R^3 = \frac{56}{3} \pi R^3$

Therefore, the density of the enlarged sphere can be calculated as:

$\rho_2 = \frac{M_2}{V_2} = \frac{\frac{32}{3} \pi R^3 \rho}{\frac{56}{3} \pi R^3} = \rho$

So, the answer is D) ρ.

Question 19

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 of a gas is inversely proportional to the square root of its molar mass. Since oxygen molecules are 16 times more massive than hydrogen molecules, their average speed will be $\sqrt{16} = 4$ times slower, not faster, than that of hydrogen molecules.

Question 20

Substance A has a density of 3 g/cm³ and substance B has a density of 4 g/cm³.In order to obtain equal masses of these two substances,what must be the ratio of the volume of A to the volume of B?

Accepted Answer

To have equal masses, the product of density and volume must be equal for both substances. Therefore, $3 \times V_A = 4 \times V_B$. Solving for the ratio $\frac{V_A}{V_B}$, we get $\frac{4}{3}$.

Quiz 10: Gases