8 exam-style questions on density, states of matter, internal energy and specific heat/latent heat. Tap Show answer for full working.
A block has mass \(0.24\,\mathrm{kg}\) and volume \(80\,\mathrm{cm}^{3}\). Calculate its density in \(\mathrm{kg\,m}^{-3}\).
\(V = 80\times10^{-6} = 8.0\times10^{-5}\,\mathrm{m}^{3}\).
\(\rho = m/V = 0.24/8.0\times10^{-5} = 3000\,\mathrm{kg\,m}^{-3}\).
Describe the arrangement and motion of particles in a solid, a liquid and a gas.
Solid: tightly packed in a regular pattern; vibrate about fixed positions.
Liquid: close together but irregular; can move past each other.
Gas: far apart; move freely at high speed in random directions.
What is meant by internal energy?
The total kinetic and potential energy of all the particles in a system.
How much energy is needed to raise the temperature of \(1.5\,\mathrm{kg}\) of aluminium by \(20^\circ\mathrm{C}\)? (Specific heat capacity of aluminium \(= 900\,\mathrm{J\,kg}^{-1}{}^\circ\mathrm{C}^{-1}\).)
\(\Delta E = mc\Delta\theta = 1.5\times900\times20 = 27\,000\,\mathrm{J}\).
Explain the difference between specific heat capacity and specific latent heat.
Specific heat capacity: energy needed to raise the temperature of \(1\,\mathrm{kg}\) of a substance by \(1^\circ\mathrm{C}\) (no change of state).
Specific latent heat: energy needed to change the state of \(1\,\mathrm{kg}\) of a substance without a change in temperature.
Explain, using the particle model, why the pressure of a gas increases when its volume is reduced at constant temperature.
Particles hit the walls more frequently (same speed, smaller volume). More frequent collisions mean a greater force on the walls and therefore higher pressure.
How much energy is needed to melt \(0.40\,\mathrm{kg}\) of ice at \(0^\circ\mathrm{C}\)? (Specific latent heat of fusion of ice \(= 334\,000\,\mathrm{J\,kg}^{-1}\).)
\(E = mL = 0.40\times334000 = 133\,600\,\mathrm{J}\) (\(1.34\times10^{5}\,\mathrm{J}\)).
A \(2.0\,\mathrm{kg}\) block of ice at \(0^\circ\mathrm{C}\) is heated until it becomes water at \(20^\circ\mathrm{C}\). Calculate the total energy required. (Specific latent heat of fusion \(= 334\,000\,\mathrm{J\,kg}^{-1}\); specific heat capacity of water \(= 4200\,\mathrm{J\,kg}^{-1}{}^\circ\mathrm{C}^{-1}\).)
To melt: \(E_1 = 2.0\times334000 = 668\,000\,\mathrm{J}\).
To heat water: \(E_2 = 2.0\times4200\times20 = 168\,000\,\mathrm{J}\).
Total \(= 836\,000\,\mathrm{J}\).