B.3 氣體定律：練習題

A fixed mass of an ideal gas is held at a constant volume. If the absolute temperature of the gas is tripled, what is the ratio of the new pressure to the original pressure of the gas?

Two containers hold different ideal gases, \(X\) and \(Y\), at the same temperature. The molar mass of gas \(Y\) is exactly four times the molar mass of gas \(X\). What is the ratio of the root-mean-square (rms) speed of the molecules in gas \(X\) to the rms speed of the molecules in gas \(Y\)?

A real gas deviates most significantly from the behavior of an ideal gas under which of the following conditions?

Which of the following describes the relationship between the volume \( V \) and the absolute temperature \( T \) of a fixed mass of an ideal gas at constant pressure?

A sample of an ideal gas is contained in a cylinder with a movable piston. The gas undergoes a process where its pressure is halved and its volume is tripled. If the initial temperature was \( T \), what is the final absolute temperature of the gas?

State the mathematical relationship between the pressure \( P \) and volume \( V \) for a fixed mass of an ideal gas at constant temperature.

Explain why the average kinetic energy of gas molecules is used as a measure of the absolute temperature of the gas.

A gas is compressed to half its original volume while its absolute temperature is increased by \( 20\% \). Determine the percentage change in the pressure of the gas.

A sample of an ideal gas is kept at a constant temperature of \( 293 \, \text{K} \) in a container with a variable volume. Initially, the volume is \( 0.040 \, \text{m}^3 \) and the pressure is \( 1.2 \times 10^5 \, \text{Pa} \).

(a) Calculate the pressure of the gas if the volume is reduced to \( 0.015 \, \text{m}^3 \).
(b) State the name of the gas law that describes this relationship between pressure and volume at constant temperature.

A rigid cylinder contains \( 0.50 \, \text{mol} \) of an ideal gas at an initial temperature of \( 27^\circ\text{C} \) and a pressure of \( 1.8 \times 10^5 \, \text{Pa} \).

(a) Calculate the volume of the cylinder.
(b) The gas is heated until the pressure becomes \( 2.4 \times 10^5 \, \text{Pa} \). Determine the final temperature of the gas in \( ^\circ\text{C} \).
(c) Explain, with reference to the kinetic theory of gases, why the pressure of the gas increases as the temperature increases for a gas at constant volume.