熱力學與理想氣體：練習題

A block of ice with a mass of \(0.50\text{ kg}\) at \(0^{\circ}\text{C}\) is heated until it melts completely into water at \(0^{\circ}\text{C}\). If the specific latent heat of fusion of ice is \(3.34 \times 10^5\text{ J kg}^{-1}\), calculate the change in the internal energy of the substance during this process, assuming no work is done against the surroundings.

An ideal gas is contained in a cylinder of volume \(V\) at a pressure \(p\). The gas contains \(N\) molecules, each of mass \(m\). Which of the following expressions correctly represents the root-mean-square speed, \(c_{\text{rms}}\), of the molecules?

A container holds an ideal gas at a temperature of \(27^{\circ}\text{C}\). If the average kinetic energy of the gas molecules is to be doubled, what must be the new temperature of the gas?

A mass of \(0.20\text{ kg}\) of a liquid is heated by an electric heater rated at \(50\text{ W}\). The temperature of the liquid increases from \(20^{\circ}\text{C}\) to \(50^{\circ}\text{C}\) in \(120\text{ s}\). Assuming that \(20\%\) of the energy supplied by the heater is lost to the surroundings, calculate the specific heat capacity of the liquid.

A sealed flask contains a mixture of Helium (molar mass \(4\text{ g mol}^{-1}\)) and Argon (molar mass \(40\text{ g mol}^{-1}\)) at thermal equilibrium. What is the ratio of the root-mean-square speed of Helium atoms to that of Argon atoms, \(\frac{v_{\text{He}}}{v_{\text{Ar}}}\)?

A cylinder contains 0.40 moles of an ideal monatomic gas. The average kinetic energy of the gas atoms is increased by \(1.2 \times 10^{-21}\text{ J}\).
Calculate the change in the root mean square speed of the atoms if their initial root mean square speed was \(450\text{ m s}^{-1}\).
(Mass of one atom \(= 6.64 \times 10^{-27}\text{ kg}\))