(455) Internal energy [IB Physics SL/HL]

Internal Energy

  • Internal energy is denoted by the variable U and is a key concept in statistical mechanics.

Equation for Ideal Gas

  • For a monatomic ideal gas, the internal energy can be expressed as:

    • U = 3nRT (using number of moles)

    • U = 3NKB (using the Boltzmann constant)

  • Where:

    • n = number of moles

    • N = number of molecules or atoms

    • R = ideal gas constant

    • KB = Boltzmann constant

    • T = temperature in Kelvin

  • Conversion between forms:

    • nR is equivalent to NKb (both formulas using different constants).

Units

  • Internal energy (U) is measured in joules.

  • Temperature (T) is measured in Kelvin.

Example Calculation

  1. Identify the equation to use based on known values:

    • If given number of molecules, use U = 3NKB.

  2. Determine the temperature in Kelvin:

    • T(K) = T(°C) + 273

    • Example conversion: For -45°C, T(K) = -45 + 273 = 228 K.

  3. Insert values into the equation:

    • Use U = 3 * (1 * 10^30) * (1.38 * 10^-23) * (228)

  4. Perform calculations to find:

    • U = 4.719 * 10^9 joules (or approximately 4.7 GJ

Key Insights

  • As temperature increases, so does internal energy.

  • The speed of molecules also influences temperature and internal energy: a higher speed correlates with higher energy levels.