Heat and Thermodynamics: Laws, Latent Heat and Transfer

The correct answer is B, the joule. Heat is a form of energy in transit, so it is measured in the same unit as work and energy, the joule, which is one newton metre.

Option A, the calorie, is an older and still familiar unit of heat, defined as the heat needed to raise the temperature of one gram of water by one degree Celsius; it equals about 4.2 joules, but it is not the SI unit. Option C, the kelvin, is the SI unit of temperature, not of heat, and the difference between heat and temperature is exactly what this question tests. Option D, the watt, is the unit of power, that is the rate of doing work or of transferring energy, one joule per second, so a heater rated in watts tells you how fast it supplies heat, not how much.

The correct answer is B, 4 degrees Celsius. Water behaves abnormally between zero and four degrees: it contracts as it is heated in that range and expands again above four degrees, so the same mass occupies its least volume, and therefore has its greatest density, at four degrees Celsius.

Option A is the freezing point, where water turns to ice; ice is in fact less dense than water, which is why it floats. Option C is the boiling point at normal atmospheric pressure, where water is at its most expanded as a liquid. Option D lies below the freezing point, where pure water at ordinary pressure is solid. The property matters in nature because in a pond in winter the water at four degrees sinks, the colder water floats and freezes at the top, and fish survive in the liquid water below.

The correct answer is B, about 540 calories per gram. This is the heat that one gram of water at a hundred degrees Celsius must absorb to become steam at the same temperature, with no rise in temperature at all; the same quantity is released when steam condenses back to water.

Option A, 80 calories per gram, is the latent heat of fusion of ice, the heat needed to melt one gram of ice at zero degrees, and interchanging the two values is the commonest error in this chapter. Option C, 336, is the same latent heat of fusion expressed in joules per gram rather than calories, offered here with the wrong unit. Option D, 2260, is the latent heat of vaporisation in joules per gram; it is the right quantity in the wrong unit, since 2260 joules is about 540 calories.

The correct answer is A, conduction and convection. Both of these modes need matter: conduction passes energy from particle to particle and convection carries it by the movement of a fluid. A vacuum has almost no particles, so neither can work across it.

Option B is wrong because radiation travels through a vacuum perfectly well, being an electromagnetic wave; the flask stops it by a different device, the silvering of the facing surfaces, which reflects the radiation back. Option C is incomplete, since the vacuum stops convection as well as conduction. Option D states the opposite of the truth. The stopper of the flask completes the design by preventing the escape of hot vapour, and this three part answer is what examiners look for. The same flask keeps a cold liquid cold for exactly the same reasons, because it blocks heat moving in as well as heat moving out.

The correct answer is A, the conservation of energy. The first law says that the heat supplied to a system is equal to the increase in its internal energy plus the external work it does. Nothing is lost and nothing is created; energy only changes its form, which is the principle of conservation applied to heat.

Option B belongs to the second law, which introduces entropy and says that it never decreases in an isolated system. Option C belongs to the zeroth law, which says that two bodies each in thermal equilibrium with a third are in equilibrium with one another and which makes the measurement of temperature possible. Option D belongs to the third law, which says that the entropy of a perfect crystal tends to zero as the temperature tends to absolute zero and that absolute zero cannot be reached.

The correct answer is A, the zeroth law. It states that if body A is in thermal equilibrium with body C, and body B is also in thermal equilibrium with body C, then A and B are in thermal equilibrium with each other. That is precisely what allows a thermometer to be used: the thermometer plays the part of the third body, and two objects that give it the same reading have the same temperature.

Option B, the first law, deals with energy accounting and not with the meaning of temperature. Option C, the second law, fixes the direction in which heat flows and sets a limit on the efficiency of engines. Option D, the third law, concerns behaviour near absolute zero. The zeroth law was recognised and named after the other three had already been numbered, which is why it carries the number zero.

The correct answer is C, radiation. The space between the sun and the earth is very nearly empty, and radiation is the only mode of heat transfer that needs no material medium: energy travels as electromagnetic waves at the speed of light and is absorbed when it strikes matter.

Option A, conduction, requires particles in contact to pass energy along, so it cannot work across empty space. Option B, convection, requires a fluid that can itself move and carry energy with it, which again is not available between the sun and the earth, though convection does distribute that heat once it has entered the atmosphere. Option D fails for both reasons. A good absorber of radiation is also a good emitter, which is why a blackened surface warms fastest in the sun.

The correct answer is A, 40 per cent. The efficiency of an ideal Carnot engine is one minus the ratio of the sink temperature to the source temperature, both in kelvin. Here the ratio is 300 divided by 500, that is 0.6, and one minus 0.6 is 0.4, which is 40 per cent.

Option B, 60 per cent, is the ratio itself rather than the efficiency, the answer of a candidate who forgets to subtract from one. Option C, 20 per cent, comes from dividing the difference of the two temperatures by their sum, which is not the formula. Option D, about 66.7 per cent, comes from dividing the source by the sink, again a misuse of the formula. Note also that the temperatures must be in kelvin; using degrees Celsius in this formula gives a wrong answer every time.

The correct answer is A. A cooker is sealed, so the steam it produces cannot escape and the pressure inside rises. Since the boiling point of a liquid rises with the pressure on it, water in a cooker boils well above a hundred degrees Celsius, and food cooking at that higher temperature is ready sooner.

Option B states the opposite and describes what happens on a mountain, where the pressure is low, water boils below a hundred degrees and cooking takes longer. Option C is wrong as a reason, and the burning power of steam comes from its latent heat rather than from specific heat. Option D is wrong because the material of the vessel affects only how quickly heat reaches the water; it cannot raise the temperature at which the water boils, which is what saves the time.

The correct answer is B, adiabatic. An adiabatic change is one in which no heat is exchanged with the surroundings. The bursting of a tyre happens so quickly that the escaping air has no time to take in or give out heat; it does work in expanding, its internal energy falls and it therefore cools, which is why the escaping air feels cold.

Option A, isothermal, is a change at constant temperature, which requires the process to be slow enough for heat to flow in or out and keep the temperature fixed. Option C, isobaric, is a change at constant pressure, such as the heating of a gas under a freely moving piston. Option D, isochoric, is a change at constant volume, such as heating a gas in a rigid closed vessel. The rise of moist air that forms cloud is another everyday adiabatic process.

The correct answer is A, one to two to three. If each length of a solid grows by a certain small fraction when it is heated, an area, which is the product of two lengths, grows by about twice that fraction, and a volume, the product of three lengths, by about three times. So the superficial coefficient is twice the linear and the cubical is three times the linear.

Option B reverses the order and would mean that a body expands least in volume, which is the opposite of what happens. Option C would be true only if area and volume did not depend on more than one length, which is not the case. Option D follows no rule at all. This ratio explains why gaps are left between rails and why a bimetallic strip of two metals with different linear coefficients bends when heated and works as a switch in a thermostat.