Question

1. if the temperature of 1 liter of an ideal gas is increased from 4 k to 16 k, which of the following describes the new average kinetic energy of the molecules of the gas?

a. twice as great
b. half as great
c. four times as great
d. one - fourth as great

1. according to kinetic molecular theory, as the temperature of a confined gas rises, which of the following characteristics of the gas molecules increases?

a. density
b. number
c. size
d. average speed

1. a mass of gas is enclosed in a rigid container. which of the following will occur if the velocity of the gas molecules colliding with the sides of the container increases?

a. the density of the gas will decrease.
b. the pressure of the gas will increase.
c. the pressure of the gas will decrease.
d. the density of the gas will increase.

Explanation:

Question 9

Step1: Recall Kinetic Energy-Temperature Relation

The average kinetic energy (\(KE_{avg}\)) of gas molecules is directly proportional to the absolute temperature (\(T\)) in Kelvin, given by \(KE_{avg} \propto T\) (from kinetic molecular theory, \(KE_{avg} = \frac{3}{2}kT\), where \(k\) is Boltzmann constant).

Step2: Calculate the Ratio of Temperatures

Initial temperature \(T_1 = 4\space K\), final temperature \(T_2 = 16\space K\). The ratio \(\frac{T_2}{T_1}=\frac{16}{4} = 4\).

Step3: Relate to Kinetic Energy

Since \(KE_{avg} \propto T\), the ratio of final to initial kinetic energy \(\frac{KE_{avg,2}}{KE_{avg,1}}=\frac{T_2}{T_1} = 4\). So the new average kinetic energy is four times as great.

According to kinetic molecular theory, temperature is related to the average kinetic energy of gas molecules (\(KE = \frac{1}{2}mv^2\), so higher \(KE\) (from higher temperature) means higher average speed (\(v\)) if mass (\(m\)) is constant. Density depends on mass and volume (constant here, so density constant). Number of molecules is constant in a confined gas. Molecule size doesn't change with temperature. So average speed increases.

In a rigid container, volume (\(V\)) and mass (\(m\)) of gas are constant, so density (\(
ho=\frac{m}{V}\)) is constant (eliminates A and D). Pressure is due to molecular collisions: higher velocity of molecules means more force per collision and more frequent collisions, so pressure increases (eliminates C).

Answer:

C. Four times as great

Question 10