Thermal energy transfers practice questions.

Which of the following best explains why metals are much better thermal conductors than non-metals?

• Free electrons in metals transfer energy rapidly through the lattice
• Metal atoms vibrate with much larger amplitudes than atoms in non-metals
• Bulk movement of the hotter regions of the metal carries energy through it
• Metals emit more infrared radiation internally than non-metals

Answer: Free electrons in metals transfer energy rapidly through the lattice

In metals, delocalised free electrons move quickly and collide with ions, transferring energy far faster than lattice vibrations alone. Bulk movement describes convection, which cannot occur in a solid.

A star radiates with constant luminosity L. An observer moves to a position twice as far from the star. The apparent brightness measured by the observer becomes:

• half its original value
• twice its original value
• one quarter of its original value
• unchanged, because luminosity is constant

Answer: one quarter of its original value

Apparent brightness b = L/(4πd²) follows an inverse-square law, so doubling d divides b by 4. Luminosity is a property of the star; brightness depends on the observer's distance.

Two blocks of equal mass, made of different solids, are heated by identical heaters of constant power. Temperature is plotted against time for each. The line for block X is steeper than the line for block Y, and neither block reaches its melting point. Which statement is correct?

• Block X has the larger specific heat capacity, because a steeper line means it stores more energy each second.
• Block X has the larger specific latent heat, because it would reach its melting point in the shorter time.
• The two specific heat capacities are equal; the gradient is fixed by the power of the heater alone.
• Block X has the smaller specific heat capacity, because the same power produces a faster temperature rise.

Answer: Block X has the smaller specific heat capacity, because the same power produces a faster temperature rise.

P = mc(ΔT/Δt), so the gradient ΔT/Δt = P/(mc): with P and m the same, a steeper line means a smaller c. Reading a steep line as 'more energy stored' inverts the relationship.

A hot copper block is dropped into cooler water in a well-insulated container and left until nothing changes any further. Which statement about the final state is correct?

• The block and the water hold the same internal energy, because energy is transferred until it is shared equally.
• The block and the water reach the same temperature, and the energy the block loses equals that the water gains.
• The final temperature is the mean of the two starting temperatures, whatever the masses of the block and the water.
• The water ends up warmer than the block, because water has the larger specific heat capacity of the two substances.

Answer: The block and the water reach the same temperature, and the energy the block loses equals that the water gains.

Thermal equilibrium means equal temperature, not equal internal energy; the shared final temperature is found from mcΔT lost = mcΔT gained, so it lies nearer the starting temperature of whichever body has the larger mc.

How much heat is needed to raise 2.0 kg of water (c = 4200 J/kg/K) by 10 K (in joules)?

Answer: 84000

Q = mc(delta T) = 2.0 × 4200 × 10 = 84000 J (84 kJ).

A temperature of 27 degrees Celsius equals how many kelvin (in K)?

Answer: 300

T(K) = T(C) + 273 = 27 + 273 = 300 K. Absolute zero is 0 K = -273 degrees Celsius.