固體、液體與氣體：練習題

A diver descends to a depth of \(25\text{ m}\) in seawater with a density of \(1030\text{ kg/m}^3\). Given that the atmospheric pressure at the surface is \(101\text{ kPa}\) and the gravitational field strength \(g = 10\text{ N/kg}\), what is the total pressure exerted on the diver?

A rectangular block of wood has a mass of \(4.5\text{ kg}\) and a volume of \(0.006\text{ m}^3\). It is placed on a flat floor on its smallest face, which has an area of \(0.015\text{ m}^2\). Calculate the pressure exerted by the block on the floor. (Take \(g = 10\text{ N/kg}\)).

A fixed mass of gas in a rigid container is heated from \(27^\circ\text{C}\) to \(327^\circ\text{C}\). Which statement correctly describes the change in the Kelvin temperature and the behavior of the gas molecules?

A bubble of air has a volume of \(2.0\text{ cm}^3\) at the bottom of a lake, where the pressure is \(300\text{ kPa}\). The bubble rises to the surface where the pressure is \(100\text{ kPa}\). Assuming the temperature of the air remains constant, calculate the volume of the bubble at the surface.

A sealed cylinder contains a gas at a pressure of \(120\text{ kPa}\) and a temperature of \(20^\circ\text{C}\). The cylinder is heated until the pressure rises to \(180\text{ kPa}\). Assuming the volume of the cylinder remains constant, calculate the final temperature of the gas in degrees Celsius.

Explain, using the kinetic theory of gases, why the pressure of a fixed mass of gas increases as its temperature is raised at a constant volume.

Calculate the pressure difference at the bottom of a water tank that is \(12\) m deep. (Density of water = \(1000\) kg/m\(^{3}\), \(g = 10\) N/kg).

A sealed container holds a fixed mass of gas at an initial pressure of \(120\text{ kPa}\) and a volume of \(0.05\text{ m}^3\) at a temperature of \(20^{\circ}\text{C}\).

(a) The gas is compressed at a constant temperature until the volume is \(0.02\text{ m}^3\). Calculate the new pressure of the gas.
(b) Explain, using the kinetic theory of matter, why the pressure increases as the volume decreases at constant temperature.
(c) What is the temperature of \(20^{\circ}\text{C}\) in Kelvin?