Gases: laws and kinetic theory：練習問題

According to the kinetic theory of gases, which of the following statements best describes the cause of gas pressure on the walls of a container?

A rigid cylinder contains a fixed mass of an ideal gas at a pressure of \(1.2 \times 10^5\text{ Pa}\) and a temperature of \(27^{\circ}\text{C}\). If the gas is cooled until its absolute temperature is reduced by one-third (\(\frac{1}{3}\)) of its original value, what is the new pressure of the gas?

According to the kinetic theory of gases, the pressure P exerted by an ideal gas in a container of volume V is related to the mean square speed (\langle c^2 \rangle\) of the gas molecules by the equation \(P V = \frac{1}{3} N m \langle c^2 \rangle\).

Which fundamental assumption of the kinetic model of an ideal gas is most directly responsible for the appearance of the factor \(\frac{1}{3}\) in this microscopic relationship?

According to the kinetic theory of gases, the absolute temperature of an ideal gas is directly proportional to the

Two vessels X and Y of volumes \(V\) and \(2V\) respectively are connected by a narrow tube of negligible volume. Initially, the vessels contain an ideal gas at a uniform pressure \(P\) and absolute temperature \(T\). Vessel X is then heated to \(2T\) while vessel Y is maintained at temperature \(T\). If no gas escapes from the system, what is the new equilibrium pressure of the gas?

State Boyle's Law regarding the relationship between the pressure and volume of a fixed mass of gas at a constant temperature.

An ideal gas is held in a container. If the root-mean-square (r.m.s.) speed of its molecules is doubled and its volume is increased to four times its original value, how does the gas pressure change?

A fixed mass of an ideal gas occupies a volume of \(0.4\text{ m}^3\) at a temperature of \(300\text{ K}\). If the temperature is increased to \(900\text{ K}\) while the pressure is kept constant, what is the new volume of the gas?

A rigid tank of volume \(0.05 \text{ m}^3\) is filled with a fixed mass of an ideal gas. Initially, the pressure inside the tank is \(1.2 \times 10^5 \text{ Pa}\) at a temperature of \(27^{\circ}\text{C}\).

(a) Calculate the number of moles of gas inside the tank.

(b) The tank is then placed in a large water bath and heated to \(87^{\circ}\text{C}\). Calculate the new pressure of the gas.

(c) Using the kinetic theory of gases, explain why the gas pressure increases as the temperature increases, provided the volume remains constant.

(Given: Universal gas constant \(R = 8.31 \text{ J mol}^{-1} \text{ K}^{-1}\))

A student conducts an experiment to investigate the properties of a fixed mass of an ideal gas contained in a cylinder with a movable piston. The initial volume of the gas is \(0.003 \text{ m}^3\) at a pressure of \(1.2 \times 10^5 \text{ Pa}\) and a temperature of \(27^{\circ}\text{C}\).

(a) Determine the number of moles of gas inside the cylinder.

(b) The gas is compressed at a constant temperature until its volume becomes \(0.0012 \text{ m}^3\). Calculate the new pressure of the gas.

(c) Starting from the state in part (b), the piston is fixed in position and the gas is heated until its pressure reaches \(4.5 \times 10^5 \text{ Pa}\). Calculate the final temperature of the gas in Celsius.

(d) State two assumptions of the kinetic model of an ideal gas.

(Given: Universal gas constant \(R = 8.31 \text{ J mol}^{-1} \text{ K}^{-1}\))