Temperature & Heat

On a cold winter morning in Kathmandu, you wrap yourself in warm clothes. When you heat water for tea, the water gets hotter. These everyday experiences involve the concepts of temperature and heat -- two related but distinct ideas in physics.

Temperature vs Heat

Temperature is a measure of the average kinetic energy of molecules in a substance. It tells us how hot or cold something is.

Heat is the total energy transferred between objects due to a temperature difference. Heat flows from a hotter body to a cooler body.

Temperature Scales

Three common scales are used:

• Celsius (C): Water freezes at 0 C, boils at 100 C
• Fahrenheit (F): Water freezes at 32 F, boils at 212 F
• Kelvin (K): Absolute scale. 0 K = -273.15 C

Conversion: C/5 = (F - 32)/9 = (K - 273)/5

Thermal Expansion

Most materials expand when heated. This is important in engineering and daily life.

Linear expansion: delta L = L alpha delta T (where alpha is the coefficient of linear expansion)

Area expansion: delta A = A beta delta T (beta = 2 alpha)

Volume expansion: delta V = V gamma delta T (gamma = 3 alpha)

Specific Heat Capacity

The amount of heat needed to raise the temperature of 1 kg of a substance by 1 C.

Q = m c delta T

where Q is heat energy (Joules), m is mass (kg), c is specific heat capacity (J/kg C), and delta T is temperature change.

Water has a high specific heat capacity (4200 J/kg C), which is why it takes longer to heat.

Calorimetry

Calorimetry is based on the principle of conservation of energy: heat lost = heat gained.

Worked Example: 200 g of water at 80 C is mixed with 300 g of water at 20 C. Find the final temperature.

Solution:

• Heat lost by hot water = Heat gained by cold water
• m1 c (T1 - T) = m2 c (T - T2)
• 0.2 x 4200 x (80 - T) = 0.3 x 4200 x (T - 20)
• 0.2 (80 - T) = 0.3 (T - 20)
• 16 - 0.2T = 0.3T - 6
• 22 = 0.5T
• T = 44 C

Nepal Connection

Thermal expansion is why gaps are left between railway tracks and in bridge joints. In Nepal, the temperature difference between summer and winter (especially in the Terai) can cause significant expansion in metal structures.

Key Takeaways

• Heat is energy transfer; temperature measures molecular kinetic energy
• Materials expand when heated (linear, area, volume)
• Q = mc delta T is the fundamental calorimetry equation
• In mixtures, heat lost by hot body = heat gained by cold body