AP Physics 2: Algebra-Based Practice Quiz: Kinetic Theory of Temperature and Pressure

Correct Answer: C

The provided content states that atoms in a gas collide with and exert forces on the container. The pressure is a result of the sum of the magnitudes of the perpendicular components of these forces exerted by the atoms on the surface.

Correct Answer: B

The content explicitly states, 'The temperature of a system is characterized by the average kinetic energy of the atoms within that system.' It is not the total energy or the energy of a single atom, but the average.

Correct Answer: C

Increased atomic speed means the atoms have more kinetic energy. When they collide with the container walls, they exert a larger force. A higher speed also means they collide with the walls more often. Both factors increase the sum of the forces on the wall, leading to higher pressure.

Correct Answer: C

The provided text specifies that pressure is 'the ratio of the sum of the magnitudes of the perpendicular components of the forces exerted by the gas's atoms on the surface to the area of the surface.' Therefore, $F_{\perp}$ represents this sum of perpendicular force components.

Correct Answer: C

Temperature is a measure of the average kinetic energy of the atoms in a system. Since both gases are at the same temperature, their atoms must have the same average kinetic energy, as described by the relation $K_{avg}=\frac{3}{2}k_{B}T$.

Correct Answer: C

The relationship between average kinetic energy and temperature is given by $K_{avg}=\frac{3}{2}k_{B}T$. This shows a direct, linear proportionality between $K_{avg}$ and $T$. Therefore, if the absolute temperature $T$ is doubled, the average kinetic energy $K_{avg}$ is also doubled.

Correct Answer: A

The relevant equation is $\frac{3}{2}k_{B}T=\frac{1}{2}mv_{rms}^{2}$. This simplifies to $T \propto v_{rms}^{2}$, or $v_{rms} \propto \sqrt{T}$. If the temperature $T$ is multiplied by 4, the root-mean-square speed $v_{rms}$ will be multiplied by $\sqrt{4} = 2$.

Correct Answer: B

The content directly links temperature to the motion of atoms: 'The temperature of a system is characterized by the average kinetic energy of the atoms within that system.' Therefore, increasing the average kinetic energy directly results in an increase in temperature.

Correct Answer: C

At constant temperature, the average speed of the atoms remains the same. However, by reducing the volume, the atoms are confined to a smaller space. This increases the rate at which they collide with the walls of the container, leading to a greater total force per unit area, and thus a higher pressure. In this case, halving the volume doubles the collision frequency, doubling the pressure.

Correct Answer: B

Since the gases are in thermal equilibrium, they are at the same temperature. This means their average kinetic energies are equal: $\frac{1}{2}m_{A}v_{rms,A}^{2} = \frac{1}{2}m_{B}v_{rms,B}^{2}$. Since Gas A is lighter ($m_{A} < m_{B}$), its speed must be greater ($v_{rms,A} > v_{rms,B}$) to maintain the equality.

Correct Answer: B

Pressure is defined as the force exerted perpendicularly on a unit area of a surface. A force component parallel to the surface would cause shear or movement along the surface, not pressure against it. The content specifies $P=\frac{F_{\perp}}{A}$, emphasizing the perpendicular component.

Correct Answer: C

The provided equation, $K_{avg}=\frac{3}{2}k_{B}T=\frac{1}{2}mv_{rms}^{2}$, explicitly equates $\frac{1}{2}mv_{rms}^{2}$ with $K_{avg}$, which is defined as the average kinetic energy for an ideal gas.

Correct Answer: C

Pressure depends on the force and frequency of collisions. While atoms of Gas X are heavier, atoms of Gas Y move faster (since $K_{avg}$ is the same). The effects of mass and speed on the total force exerted on the walls cancel out. For ideal gases under these conditions (same number of particles, volume, and temperature), the pressure will be the same.

Correct Answer: A

Pressure is defined as $P=\frac{F_{\perp}}{A}$. If the force $F_{\perp}$ remains constant and the area $A$ is doubled to $2A$, the new pressure will be $P_{new} = \frac{F_{\perp}}{2A} = \frac{1}{2} (\frac{F_{\perp}}{A}) = P/2$.

Correct Answer: B

Tripling the average kinetic energy ($K_{avg}$) means the absolute temperature ($T$) is also tripled, since $K_{avg} \propto T$. For an ideal gas in a fixed volume, pressure is directly proportional to temperature ($P \propto T$). Therefore, tripling the temperature will also triple the pressure.