Thermal Physics - Formula Sheet

Essential Mathematical Formulas

This reference sheet contains the mathematical expressions and equations governing thermal expansion, temperature scales, gas laws, and thermodynamic states.

1. Temperature Scale Relations

K = C + 273

K = (F + 460) * 5 / 9

• K: Temperature in Kelvin (absolute SI unit)
• C: Temperature in degrees Celsius
• F: Temperature in degrees Fahrenheit

2. Thermal Expansion in Solids

Delta L = alpha_L * L0 * Delta T

Delta A = alpha_A * A0 * Delta T

Delta V = alpha_V * V0 * Delta T

• Delta L, Delta A, Delta V: Change in length, area, and volume respectively
• L0, A0, V0: Original length, area, and volume at initial temperature
• alpha_L, alpha_A, alpha_V: Coefficients of linear, superficial, and cubical expansion (K^-1)
• Delta T: Temperature change (T_final - T_initial)

3. Liquid Expansion Relations

Real Expansion = Apparent Expansion + Container Expansion

L3 - L2 = (L3 - L1) + (L1 - L2)

• L1: Initial level of the liquid in the flask at room temperature
• L2: Lowest level of the liquid after the flask expands on heating
• L3: Final level of the liquid after thermal expansion of the liquid takes place

4. Boyle's Law

P * V = constant (at constant temperature)

P1 * V1 = P2 * V2

• P: Pressure of the gas
• V: Volume of the gas

5. Charles's Law (Law of Volume)

V / T = constant (at constant pressure)

V1 / T1 = V2 / T2

• V: Volume of the gas
• T: Absolute temperature of the gas in Kelvin

6. Avogadro's Law

V / n = constant (at constant temperature and pressure)

• V: Volume of the gas
• n: Number of moles or molecules in the gas

7. Ideal Gas Equation

P * V = R * T (for 1 mole of gas)

P * V = n * R * T (for n moles of gas)

P * V = mu * N_A * kB * T

• P: Pressure of the gas
• V: Volume of the gas
• n (or mu): Number of moles of the gas
• R: Universal gas constant (8.31 J mol^-1 K^-1)
• kB: Boltzmann's constant (1.38 * 10^-23 J K^-1)
• N_A: Avogadro's number (6.023 * 10^23 mol^-1)
• T: Absolute temperature in Kelvin