Heat and thermodynamics basics for NDA

Heat is the chapter where NDA physics sounds most like daily life. Why does a pressure cooker save time? Why does steam scald worse than boiling water? Why do earthen pots keep water cool, and why are two thin blankets warmer than one thick one? The syllabus names the effects of heat, measurement of temperature and heat, change of state and latent heat, and modes of transfer of heat, and it lists the pressure cooker and the thermos flask among the devices.

Most questions are conceptual, with a few short numericals: a scale conversion, Q = mcΔT, a latent-heat calculation or a mixing problem. The conversions come up often enough that you should be able to do them in your head.

Typical question types are:

• heat versus temperature, and conversions between °C, °F and K;
• choice of thermometer and thermometric liquid;
• thermal expansion in daily life, and the anomalous expansion of water;
• specific heat and why water's high value matters;
• latent heat, evaporation and cooling;
• the effect of pressure and impurities on boiling and melting points;
• conduction, convection and radiation, with examples;
• the first and second laws of thermodynamics, and refrigerators.

Heat and temperature

Heat is energy that flows from one body to another because of a temperature difference. Its SI unit is the joule; the older unit, the calorie, is about 4.2 J. Temperature is a measure of how hot a body is, and it decides the direction of heat flow. Heat flows from higher to lower temperature, never on its own the other way.

A bucket of warm water holds more heat than a cup of boiling water, but the cup is at the higher temperature. Heat depends on the amount of matter; temperature does not.

Temperature scales and thermometers

Conversions: K = °C + 273.15 (273 in most questions); °F = (9/5)°C + 32, or C/5 = (F − 32)/9. The Celsius and Fahrenheit scales read the same at −40°. A change of 1 °C equals a change of 1 K but 1.8 °F.

• A clinical thermometer has a short range (roughly 35 °C to 42 °C) and a kink that stops the mercury falling back.
• Mercury is a good thermometric liquid: it expands uniformly, is opaque and easy to see, does not wet glass, and stays liquid over a wide range (freezing at about −39 °C). For very cold places, alcohol is used because it freezes at a much lower temperature.
• A pyrometer measures very high temperatures, such as those of furnaces, from the radiation they give off.

Thermal expansion

Most substances expand on heating. Solids expand least, liquids more, gases most.

• Gaps are left between rails and in bridges (expansion joints); telephone and power lines sag in summer.
• A tight metal lid on a glass jar loosens in hot water because the metal expands more than the glass.
• Thick glass cracks when hot water is poured in, because the inner surface expands before the outer. Borosilicate (Pyrex) glass expands very little, so it resists this.
• A bimetallic strip of two metals that expand differently bends when heated. It is used in thermostats (irons, heaters) and fire alarms.

The anomalous expansion of water. Between 0 °C and 4 °C, water contracts on heating. It is densest at 4 °C. So in winter the surface water of a lake cools, sinks until the whole lake is at 4 °C, and then the top layer cools further and freezes. Ice, being lighter, floats and insulates the water below, and fish survive. Water also expands by about 9% on freezing, which is why water pipes burst in severe cold.

Specific heat

The heat needed to raise the temperature of 1 kg of a substance by 1 °C (or 1 K) is its specific heat capacity c. The heat needed for a mass m and a rise ΔT is:

Q = m c ΔT

Water has an unusually high specific heat, about 4,200 J/kg K (1 cal/g °C). It heats and cools slowly, and it stores a lot of heat. So:

• water is used as the coolant in car radiators and in hot-water bottles;
• coastal places have milder climates than inland ones;
• land heats faster than the sea by day and cools faster by night, which drives sea and land breezes.

Latent heat and change of state

During melting or boiling, the temperature stays constant while heat is absorbed. This heat, which goes into changing the state, is latent heat: Q = mL.

• Latent heat of fusion of ice: about 3.36 × 10⁵ J/kg (80 cal/g).
• Latent heat of vaporisation of water: about 2.26 × 10⁶ J/kg (540 cal/g).

Steam at 100 °C burns more severely than water at 100 °C because each kilogram of steam gives out an extra 2.26 × 10⁶ J as it condenses on the skin. For the same reason, ice at 0 °C cools a drink better than water at 0 °C.

Evaporation is the escape of molecules from a liquid's surface at any temperature, and it causes cooling because the fastest molecules leave. It is quicker with a larger surface area, higher temperature, lower humidity and more wind. This explains cooling by sweating, water kept cool in an earthen pot, and why humid days feel sticky: sweat evaporates slowly.

Boiling, melting and pressure

• Boiling point rises with pressure. In a pressure cooker the trapped steam raises the pressure, water boils well above 100 °C, and food cooks faster.
• Boiling point falls with lower pressure. At high altitude water boils below 100 °C, so cooking takes longer. Mountaineers and soldiers posted at heights use pressure cookers for this reason.
• Impurities such as salt raise the boiling point and lower the freezing point. Salt spread on icy roads, and a mixture of ice and salt used to make ice cream, both rely on this.
• The melting point of ice falls with pressure. Pressing two ice cubes together makes them stick when released (regelation).

The three modes of heat transfer

• Metals are good conductors; wood, plastic, wool and still air are poor conductors. Woollen clothes and two thin blankets keep us warm because they trap layers of air. Igloos stay warm inside because packed snow holds air.
• Dark, dull surfaces absorb and emit radiation well; white, shiny surfaces reflect it. So white clothes are cooler in summer, and cooking pots are blackened at the bottom.
• A thermos (vacuum) flask cuts all three: the vacuum between the double walls stops conduction and convection, the silvered walls reduce radiation, and the stopper blocks convection out of the mouth.
• Newton's law of cooling: a body cools at a rate roughly proportional to the temperature difference between it and its surroundings, so hot tea cools fastest at first.

Thermodynamics in brief

• Zeroth law: two bodies each in thermal equilibrium with a third are in equilibrium with each other. This is what makes a thermometer meaningful.
• First law: energy is conserved. Heat supplied = increase in internal energy + work done by the system.
• Second law: heat does not flow by itself from a colder to a hotter body, and no heat engine can turn all the heat it takes in into work. No engine is 100% efficient.

A refrigerator or air conditioner moves heat from a cold space to warmer surroundings, and it needs work (electricity) to do so. A refrigerator with its door left open in a closed room warms the room, because it dumps the heat it removes plus the energy of the motor into the same room.

Worked NDA-style MCQs

Q1. 25 °C on the Fahrenheit scale is:
(a) 45 °F (b) 57 °F (c) 77 °F (d) 13 °F

(9/5) × 25 + 32 = 45 + 32 = 77 °F. Answer: (c).

Q2. At what temperature is the Fahrenheit reading twice the Celsius reading?
(a) 40 °C (b) 80 °C (c) 160 °C (d) −40 °C

1.8C + 32 = 2C gives 0.2C = 32, so C = 160 °C and F = 320 °F. Answer: (c).

Q3. The heat needed to raise 2 kg of water from 20 °C to 70 °C (c = 4,200 J/kg K) is:
(a) 42 kJ (b) 210 kJ (c) 420 kJ (d) 840 kJ

Q = 2 × 4,200 × 50 = 420,000 J = 420 kJ. Answer: (c).

Q4. The heat needed to melt 0.5 kg of ice at 0 °C (L = 3.36 × 10⁵ J/kg) is:
(a) 1.68 × 10⁵ J (b) 3.36 × 10⁵ J (c) 6.72 × 10⁵ J (d) 1.68 × 10⁴ J

Q = mL = 0.5 × 3.36 × 10⁵ = 1.68 × 10⁵ J. The temperature stays at 0 °C throughout. Answer: (a).

Q5. 2 kg of water at 20 °C is mixed with 1 kg of water at 80 °C. Ignoring heat losses, the final temperature is:
(a) 50 °C (b) 40 °C (c) 60 °C (d) 30 °C

Heat lost = heat gained: 1 × (80 − T) = 2 × (T − 20), so 80 − T = 2T − 40, 3T = 120 and T = 40 °C. Answer: (b).

Q6. A lake freezes in winter. The temperature of the water just above the bottom is about:
(a) 0 °C (b) −4 °C (c) 4 °C (d) 100 °C

Water at 4 °C is densest and sinks, staying below the ice. Answer: (c).

Common mistakes

• Using heat and temperature as synonyms. Heat is energy in transit; temperature is its "level".
• Adding 32 before multiplying. °F = (9/5)°C + 32, in that order.
• Saying water is densest at 0 °C. It is densest at 4 °C; ice is lighter.
• Thinking a pressure cooker adds heat faster. It raises the boiling point, so the cooking temperature is higher.
• Believing an open fridge cools a closed room. It warms it.

Practice set

1. Absolute zero on the Celsius scale is: (a) 0 °C (b) −100 °C (c) −273.15 °C (d) −459 °C
2. 104 °F on the Celsius scale is: (a) 36 °C (b) 40 °C (c) 42 °C (d) 72 °C
3. A thermostat in an electric iron commonly uses: (a) a thermocouple (b) a bimetallic strip (c) a mercury column (d) a fuse
4. Heat from the Sun reaches the Earth by: (a) conduction (b) convection (c) radiation (d) all three
5. The heat needed to raise 1 kg of water from 10 °C to 30 °C (c = 4,200 J/kg K) is: (a) 4,200 J (b) 42,000 J (c) 84,000 J (d) 126,000 J
6. On a sunny afternoon, the breeze at a beach usually blows: (a) from land to sea (b) from sea to land (c) parallel to the coast (d) not at all
7. Water in an earthen pot stays cool because of: (a) conduction (b) evaporation (c) radiation (d) convection
8. Dissolving salt in water: (a) lowers its boiling point (b) raises its boiling point (c) does not change it (d) raises its freezing point

Answers:

1. (c). 0 K.
2. (b). (104 − 32) × 5/9 = 72 × 5/9 = 40.
3. (b). It bends and breaks the circuit at the set temperature.
4. (c). Space has no medium for conduction or convection.
5. (c). 1 × 4,200 × 20.
6. (b). Land heats faster; the air over it rises and cooler sea air flows in.
7. (b). Water seeps through the pores and evaporates, taking latent heat from the pot.
8. (b). It also lowers the freezing point.

What to do next

• Do ten scale conversions each way (°C to °F and back, °C to K) without writing anything down.
• List ten everyday examples and label each conduction, convection, radiation, evaporation or latent heat.
• Solve five Q = mcΔT, five Q = mL and three mixing problems.
• Revise properties of matter for pressure, then continue to waves and sound.