When we heat a body, its temperature rises and it may also expand or change state. This chapter covers temperature scales, thermal expansion, heat capacity, and modes of heat transfer.
Temperature and Its Measurement
Temperature is a measure of the average kinetic energy of molecules. It determines the direction of heat flow — from higher to lower temperature.
- Thermometric scales:
- Celsius (C): ice point = 0C, steam point = 100C
- Fahrenheit (F): ice point = 32F, steam point = 212F
- Kelvin (K): T(K) = T(C) + 273.15 (SI scale; absolute zero = 0 K)
- Conversion: F = (9/5)C + 32; C = (5/9)(F - 32)
Thermal Expansion
Solids, liquids, and gases expand on heating.
Linear expansion: deltaL = alpha L0 deltaT. Coefficient of linear expansion alpha (unit: /K or /C).
Area expansion: deltaA = 2 alpha A0 deltaT (beta = 2 alpha)
Volume expansion: deltaV = gamma V0 deltaT (gamma = 3 alpha for solids)
Anomalous expansion of water: Water contracts on heating from 0C to 4C, and then expands. Maximum density of water is at 4C. This protects aquatic life in winter.
Specific Heat Capacity
Heat absorbed/released: Q = m c deltaT
where c = specific heat capacity (J/kg/K), m = mass, deltaT = temperature change.
Molar heat capacity: C = Q / (n deltaT), where n = number of moles.
Water equivalent of a body = mass of water that absorbs the same heat for the same temperature rise.
Principle of Calorimetry: Heat lost by hot body = Heat gained by cold body (in an isolated system).
m1 c1 (T1 - T) = m2 c2 (T - T2)
Change of State
- Latent Heat (L): Heat absorbed or released during a change of state without change in temperature.
- Q = m L
- Latent heat of fusion (Lf) for ice = 3.34 x 105 J/kg
- Latent heat of vaporisation (Lv) for water = 22.6 x 105 J/kg
During melting/boiling temperature remains constant while heat is continuously supplied.
Modes of Heat Transfer
Conduction: Heat transfer through a medium without bulk movement of matter.
Rate of heat flow: Q/t = K A (T1 - T2) / d
where K = thermal conductivity, A = area, d = thickness.
Convection: Heat transfer by actual movement of heated fluid (e.g., sea breeze, monsoons, room heaters).
Radiation: Heat transfer without any medium; energy travels as electromagnetic waves (infrared). Stefan-Boltzmann law: P = sigma A e T4
where sigma = 5.67 x 10-8 W/m2/K4, e = emissivity.
Newton's Law of Cooling: Rate of cooling is proportional to the excess temperature of a body over its surroundings: dT/dt = -k(T - Ts). Valid for small temperature differences.
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Convert 37C (body temperature) to Fahrenheit and Kelvin.
F = (9/5)(37) + 32 = 66.6 + 32 = 98.6 F
K = 37 + 273 = 310 K
A steel rail of length 30 m at 20C. alpha = 1.2 x 10-5 /C. Find expansion at 50C.
deltaL = alpha L0 deltaT = 1.2 x 10-5 x 30 x 30 = 1.08 x 10-2 m = 1.08 cm
200 g of water at 80C is mixed with 100 g of water at 20C. Find final temperature (cwater = 4200 J/kg/K).
Heat lost = Heat gained: 200 x 4200 x (80-T) = 100 x 4200 x (T-20)
2(80-T) = T-20 => 160-2T = T-20 => 3T = 180 => T = 60C
How much heat is needed to melt 500 g of ice at 0C? (Lf = 3.34 x 105 J/kg)
Q = m L = 0.5 x 3.34 x 105 = 1.67 x 105 J
A glass window pane (K = 0.8 W/m/K, thickness 4 mm, area 1.5 m2) separates room at 25C from outside at 5C. Find rate of heat loss.
Q/t = K A deltaT / d = 0.8 x 1.5 x 20 / 0.004 = 6000 W
A blackbody at 500 K radiates. (sigma = 5.67 x 10-8 W/m2/K4, A = 0.1 m2). Find power radiated.
P = sigma A T4 = 5.67 x 10-8 x 0.1 x (500)4 = 5.67 x 10-8 x 0.1 x 6.25 x 1010 = 354 W
A body cools from 60C to 50C in 5 min; surroundings at 25C. Using Newton's law, find time to cool from 50C to 45C.
Average temperature in first case = 55C; excess = 30C; Rate = 10/5 = 2C/min
Average temperature in second case = 47.5C; excess = 22.5C
Time = (5/10) x (22.5/30 x 10/2) ... using proportionality: t = 5 x (22.5/30) / (22.5/30) is ratio based: t = 5 x (22.5/30) x (30/10) x (5/10)... Simplified: t = 5 x (22.5/30) / 1 ~ 3.75 min
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Common mistakes
- Do NOT add 273 when converting C to F — only C to K requires adding 273.
- Latent heat involves no temperature change — adding heat during melting does NOT raise temperature until the phase change is complete.
- For calorimetry, remember that heat lost by hot = heat gained by cold (in a perfectly insulated system).
Summary
Temperature drives heat flow. Thermal expansion coefficients relate dimensional changes to temperature. Specific heat and latent heat describe energy stored in matter. Conduction, convection, and radiation are the three modes of heat transfer, each governed by distinct laws.