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## Thermal Energy

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**Atomic Motion**• The macroscopic properties of a system are based on the microscopic behavior of atoms. Macroscopic equation of state: pressure, volume, temperature Microscopic laws of motion: position, velocity, energy**Ideal Gas Energy**• Kinetic theory supplies the energy for an ideal gas. • Kav = (3/2)kT • Convert this to the total system energy. • U = (3/2)NkT • U = (3/2)nRT • This energy is internal to the gas. Energy based on temperature and number of molecules**Internal Energy**• The kinetic energy of an ideal gas is its internal energy. • Also called thermal energy • Internal energy does not include energy from external measures. • Center of mass translation • Rigid body rotation • Potential from external force vCM Fext**Vibrations**• Mean particle speed is not the only source of internal energy. • Real molecules can have internal motion. • Rotation • Vibration • These effects add to internal energy. Rotation around center of mass Vibration at center of mass**Energy Transfer**• Thermal energy changes in a system. • It flows in and out • Due to changes in macroscopic properties • When it is due to temperature changes it is called heat. Heat flow**Work is a process that represents the change in the**mechanical energy. Force acting through a distance Measured in joules like energy Heat is a process that represents the change in the thermal energy. Due to a difference in temperature Measured in joules like energy Heat and Work**Mechanical Equivalent**• In the 1800’s James Joule demonstrated that mechanical work could cause a change in temperature. • Heat, like work, represented a change in energy.**Heat was measured by a change in temperature.**1 calorie (cal) is the amount of heat needed to raise 1 g of water by 1 C. 1 kcal = 1000 cal, and is what we call a “Calorie” for food. Calories (or kcal) are often used to measure heat or internal energy. Since SI has a unit of energy (J) it remains the unit for all forms of energy. Work Mechanical energy Potential energy Dissipative energy Heat Thermal energy Internal energy 1 cal = 4.186 J Calorie**You gobble too much ice cream and decide to walk up stairs**to burn the additional 500 Calories. If your mass is 60 kg, what vertical height must you climb? Convert to joules from kcal. W = (500 kcal)(1000 cal/kcal)(4.186 J/cal) W = 2.1 x 106 J. Work climbing is W = mgh. h = W / mg = (2.1 x 106 J) / (60 kg)(9.8 m/s2) h = 3600 m. Real humans are inefficient and h is closer to 700 m. Burn It next