熱能傳遞：練習題

In the ideal gas equation \( pV = nRT \), what does the symbol \( n \) represent?

What is the average kinetic energy of a single molecule of an ideal gas at temperature \(T\)?

A sample of gas undergoes an adiabatic expansion. During this process, the gas does 500 J of work on its surroundings. What is the change in the internal energy of the gas?

The pressure of an ideal gas is \(P\) and its volume is \(V\). If the temperature remains constant and the volume is increased to \(3V\), what is the new pressure?

An ideal gas has a root-mean-square (rms) speed of molecules equal to \( c_{rms} \) at temperature \( T \). If the absolute temperature of the gas is tripled, what is the new rms speed?

Describe the change, if any, in the kinetic energy and potential energy of the molecules in a substance during a change of state at a constant temperature.

An ideal gas is contained in a cylinder of volume \( V \) at pressure \( P \). If the number of molecules is doubled and the absolute temperature is halved, calculate the new pressure in terms of \( P \).

Explain why the temperature of a substance remains constant during a change of state, such as melting, even though thermal energy is being supplied.

A sample of 2.0 moles of an ideal gas is kept at a constant temperature of 300 K. The volume of the gas is decreased from \(0.040\,\text{m}^3\) to \(0.020\,\text{m}^3\).
(a) Calculate the initial pressure of the gas.
(b) Determine the final pressure of the gas, assuming the temperature remains constant.

A container of volume \(0.50\,\text{m}^3\) contains \(4.0 \times 10^{23}\) molecules of helium at a pressure of \(1.0 \times 10^5\,\text{Pa}\). Helium behaves as an ideal gas.
(a) Calculate the temperature of the gas.
(b) Calculate the average kinetic energy of a single helium molecule.
(Boltzmann constant \(k = 1.38 \times 10^{-23}\,\text{J}\,\text{K}^{-1}\))