Lesson 14: Measurement and Effects of Heat

In the figure : In the figure heat required = mass × rise in temperature (for water, in cal). 200 g of water heated from 25 °C to 75 °C needs 200 × 50 = 10000 cal, which is 10000 × 4.18 = 41800 J.

Rule 1: Units and calculation — The SI unit of heat is the joule (J) and the CGS unit is the calorie (cal). 1 calorie = 4.18 joule. One calorie is the heat needed to raise the temperature of 1 g of water by 1 °C. For water: heat required (cal) = mass (g) × rise in temperature (°C).

• Easy : 100 g water heated by 10 °C needs 100 × 10 = 1000 cal.
• Medium : 500 g water from 20 °C to 60 °C: 500 × 40 = 20000 cal = 20000 × 4.18 = 83600 J.
• Exam-type : 2 kg (2000 g) water from 10 °C to 35 °C: 2000 × 25 = 50000 cal = 50000 × 4.18 = 209000 J.

In the figure : In the figure the sources of heat are: A the Sun (fusion of hydrogen nuclei), B the earth (geothermal energy), C burning fuel (chemical energy), D an electric heater (electrical energy), E a nuclear reactor (fission of uranium).

Rule 2: Sources of heat — The Sun (fusion of hydrogen nuclei into helium), the earth (geothermal energy), chemical energy (burning fuels with oxygen), electrical energy (electric press, heater), atomic energy (fission of uranium, thorium) and the air.

• Easy : Cooking gas gives heat by chemical energy.
• Medium : An electric iron gives heat from electrical energy.
• Exam-type : Hot water springs show the earth's own heat (geothermal energy).

Spot the difference

In the figure : In the figure our sense of hot and cold is relative. After the left hand is in cold water P and the right hand in hot water R, the room-temperature water Q feels warm to the left hand and cold to the right hand.

Rule 1: Why a thermometer — Our sense of hot and cold is relative. A thermometer has a narrow glass tube with a bulb filled with a liquid (earlier mercury, now alcohol) that expands and rises when heated.

• Easy : A glass of lukewarm water can feel hot or cold depending on your hand.
• Medium : The liquid in a thermometer rises because it expands on heating.
• Exam-type : Broken mercury thermometers are dangerous; do not touch the mercury and tell an adult.

In the figure : In the figure a clinical thermometer measures temperatures from 35 °C to 42 °C. The temperature of a healthy body is 37 °C.

Rule 2: Types of thermometers — A clinical thermometer measures 35 °C to 42 °C (healthy body 37 °C). Digital thermometers use a sensor. The maximum-minimum thermometer records the extremes of a day.

• Easy : A reading of 39 °C on a clinical thermometer means fever.
• Medium : A clinical thermometer cannot measure 100 °C because it is limited to 42 °C.
• Exam-type : The maximum-minimum thermometer helps weather offices record a day's highest and lowest temperature.

In the figure : In the figure on the two scales 0 °C = 32 °F, 100 °C = 212 °F, and −40 °C = −40 °F. Use (F − 32)/9 = C/5 and K = C + 273.15.

Rule 3: Temperature scales — Scales: Celsius, Fahrenheit and Kelvin (Kelvin is used in scientific work). (F − 32)/9 = C/5 and K = C + 273.15. Water boils at 212 °F, 100 °C, 373.15 K and freezes at 32 °F, 0 °C. The value is the same on both scales at −40.

• Easy : 37 °C = 37 × 9 ÷ 5 + 32 = 98.6 °F.
• Medium : 86 °F: (86 − 32) ÷ 9 = 6, C = 6 × 5 = 30 °C, K = 30 + 273.15 = 303.15.
• Exam-type : 104 °F: (104 − 32) ÷ 9 = 8, C = 8 × 5 = 40 °C. At −40 °C: −40 × 9 ÷ 5 + 32 = −72 + 32 = −40 °F.

Spot the difference

In the figure : In the figure heat is the total kinetic energy of the atoms and temperature is related to their average kinetic energy. The atoms of a solid oscillate about fixed positions, more strongly at 80 °C (Q) than at 20 °C (P).

Rule 1: Heat versus temperature — Atoms of a solid oscillate about fixed positions, faster at higher temperature. Of two objects of the same substance at equal temperature, the one with twice the mass has twice the heat content.

• Easy : Two cups of water at 60 °C: the one with twice the water has twice the heat.
• Medium : A large pot and a small cup at the same temperature have equal temperature but unequal heat.
• Exam-type : Sparks from a grinder are very hot but their tiny mass carries very little heat.

In the figure : In the figure when a hot object touches a cold object, heat flows from the hot to the cold object until their temperatures become equal.

Rule 2: Specific heat — When a hot and a cold object touch, heat flows until their temperatures become equal. Q = m × c × (T_f − T_i). Specific heats in cal/(g °C): water 1.0, alcohol 0.58, aluminium 0.21, iron 0.11, copper 0.09.

• Easy : Water has the highest specific heat in the list: it takes the most heat to warm.
• Medium : Aluminium 200 g from 20 °C to 70 °C: Q = 200 × 0.21 × 50 = 2100 cal.
• Exam-type : Copper 50 g heated by 100 °C: Q = 50 × 0.09 × 100 = 450 cal. Water of 50 g heated by 100 °C needs 50 × 1 × 100 = 5000 cal, about 11 times more.

In the figure : In the figure of a calorimeter A is the thermometer, B the stirrer, C the inner copper vessel, D the outer vessel and E the water. The air gap isolates the inner vessel, so heat lost by the hot object equals heat gained by the water and the calorimeter.

Rule 3: Calorimeter — A calorimeter (उष्मामापक) measures heat content. It has an inner copper vessel and an outer vessel (thermally isolated), a thermometer and a stirrer. Heat lost by the hot object = heat gained by the water and the calorimeter.

• Easy : Stirring makes the temperature even in the water.
• Medium : If 100 g of water at 20 °C is mixed with 100 g of water at 80 °C, the final temperature is the middle value 50 °C.
• Exam-type : In that mixing, heat lost = 100 × 30 = 3000 cal and heat gained = 100 × 30 = 3000 cal: they are equal.

Spot the difference

In the figure : In the figure a solid expands on heating (dashed outlines): linear expansion is the increase in length, areal expansion the increase in area and volumetric expansion the increase in volume.

Rule 1: Three kinds of expansion — Solids, liquids and gases all expand on heating. A rod gets longer (linear), a sheet gets bigger (areal) and a block gets bigger in volume (volumetric).

• Easy : A heated iron ring becomes slightly larger.
• Medium : A metal lid stuck on a jar loosens when dipped in hot water, because the lid expands.
• Exam-type : Electric wires sag more in summer because they become longer.

In the figure : In the figure the increase in length is proportional to the original length and to the rise in temperature, so the 2 m rod lengthens twice as much as the 1 m rod: l₂ = l₁(1 + λΔT).

Rule 2: Linear expansion formula — l₂ = l₁(1 + λΔT), where λ is the coefficient of linear expansion (unit 1/°C): the change in length of a rod of unit length for a rise of 1 degree. Among copper, aluminium, iron and silver it is highest for aluminium (23.1 × 10^-6).

• Easy : Increase in length = l₁ × λ × ΔT.
• Medium : A 2 m aluminium rod heated by 50 °C: increase = 2 × 23.1 × 10^-6 × 50 = 2.31 × 10^-3 m = 2.31 mm.
• Exam-type : A 100 m aluminium wire heated by 40 °C: increase = 100 × 23.1 × 10^-6 × 40 = 0.0924 m = 9.24 cm.

In the figure : In the figure gaps are left between rails (and provision is made in bridges) because they expand in summer. The 12 mm gap shrinks to 4 mm in hot weather, and rails with no gap bend (R).

Rule 3: Why gaps are left — Gaps are left between rails, and provision is made in bridges, because of expansion in summer. The 18 km long Great Belt Bridge in Denmark gets 4.7 m longer in summer.

• Easy : A 12 mm gap closes to 4 mm: the rails expanded 12 − 4 = 8 mm.
• Medium : 4.7 m on 18 km (18000 m) is a small part: 4.7 ÷ 18000 is about 0.00026, or 0.026 percent.
• Exam-type : Rails with no gap would bend in summer, so engineers always leave a gap.

Spot the difference

In the figure : In the figure liquids expand on heating, and different liquids expand by different amounts (the level rises the most in P). Water behaves differently from other liquids: its behaviour is anomalous.

Rule 1: Expansion of liquids — A liquid has no definite shape but a definite volume, so a volumetric expansion coefficient is defined: alcohol 1.0, chloroform 1.3, water 0.2, mercury 0.2 (× 10^-3 per °C). Water behaves differently from the others: between 0 °C and 4 °C it contracts on heating.

• Easy : Alcohol expands more than water for the same rise.
• Medium : 1000 mL of alcohol heated by 20 °C expands by 1000 × 1.0 × 10^-3 × 20 = 20 mL.
• Exam-type : 500 mL of mercury heated by 50 °C expands by 500 × 0.2 × 10^-3 × 50 = 5 mL.

In the figure : In the figure a gas heated at constant pressure expands (the piston rises). The number of particles is the same, so its density decreases. In a closed box the gas cannot expand, so its pressure increases.

Rule 2: Expansion of gases — A gas has no fixed volume. In a closed box its pressure increases on heating. Its expansion is measured at constant pressure: hydrogen 3.66, helium 3.66, nitrogen 3.67, sulphur dioxide 3.90 (× 10^-3 per °C). The density of a gas decreases on heating.

• Easy : Hot air balloons rise because heated air has lower density.
• Medium : 1000 mL of hydrogen at 0 °C heated by 10 °C expands by 1000 × 3.66 × 10^-3 × 10 = 36.6 mL.
• Exam-type : A sealed can or spray container must not be heated or left in the sun, because the gas pressure rises and it can burst.

Spot the difference