Distinguish between internal energy and thermal energy (heat).

Internal energy:

Thermal energy:

A 300 W immersion heater is placed in a beaker containing 0.25 kg of water at a temperature of 18°C. The heater is switched on for 120 s, after which time the temperature of the water is 45°C. The thermal capacity of the beaker is negligible and the specific heat capacity of water is 4.2×10³J kg^–1K^–1.

(i) Estimate the change in internal energy of the water.

(ii) Determine the rate at which thermal energy is transferred from the water to the surroundings during the time that the heater is switched on.

The water in (b) is further heated until it starts to boil at constant temperature. It is boiled for 500s measured from the time that it first starts to boil. The mass of water remaining after this time is 0.20kg.

(i) Estimate, using the answer to (b)(ii), the specific latent heat of vaporization of the water.

(ii) Explain, in terms of the energy of the molecules of the water, why the water boils at constant temperature.

internal energy:

the sum of the potential and the (random) kinetic energy of the molecules/particles of a substance;

Allow “potential and kinetic” for “sum”.

thermal energy:

the (non-mechanical) transfer of energy between two different bodies as a result of a temperature difference between them;

(i) (ΔU)=0.25×4.2×10³×27(=2.835×10⁴J);
=2.8×10⁴(J);
Award [2] for a bald correct final answer of 28 (kJ)
Award [1 max] if correct energy calculated but the answer goes on to work out a further quantity, for example power.

(ii) energy transfer=[300×120] – [2.835×10⁴]=7.65×10³ (J);
rate of transfer=\(\frac{{7.650 \times {{10}^3}}}{{120}} = 64\left( {\rm{W}} \right)\);
Allow ECF from (b)(i).

Award [1 max] for \(\frac{{(b)(i)answer}}{{120}}\) where answer omits 300×120 term, however only allow this if 120 is seen. Award [0] for other numerators and denominators.
Accept rounded value from (b)(i) to give 67 (W). 

(i) total energy supplied to water=(500×300–500×64=)1.18×10⁵(J) ;

specific latent heat\( = \left( {\frac{Q}{m} = \frac{{1.18 \times {{10}^5}}}{{0.05}} = } \right)2.4 \times {10^6}{\rm{Jk}}{{\rm{g}}^{ - 1}}\);

Award [1 max] for \(\frac{{500 \times {\rm{answer to (b)(ii)}}}}{{0.05}}\).

(ii) all the thermal energy is used to separate the molecules/break the bonds between molecules; and not to increase their (average) kinetic energy; average kinetic energy is a measure of the temperature (of the water);

There was a widespread failure to respond to the command term. “Distinguish” implies some type of comparison but often candidates simply gave definitions (which could in this mark scheme attract full credit). However, only a few received two marks. Explanations of the meaning for thermal energy were weak and usually failed to make clear the need for a temperature difference in the transfer of the energy.

(i) Many were able to access both marks, but some lost credit by then inserting an extra final step and going part way to the solution to (ii). As these candidates did not fully understand what was meant by “change in internal energy” they could not achieve full marks for this part question.

(ii) This part question was more poorly done than (i). Incorrect solutions included: failures to subtract the 28 kJ arrived at in (b)(i), and incorrect arithmetic.

(i) This was poorly done with most candidates unable to calculate the mass of water that had been vaporized.

(ii) The part question invites the candidates to consider the energy of the molecules and to link this to the constant temperature of the boiling water. Responses were mostly unfocussed with few candidates able to put forward a logical or clearly articulated explanation.