Thermal physics

• The internal energy of a system is the sum of the kinetic and potential energies of all the particles in the system.
• The internal energy of a system can be increased by doing work on the system or by increasing the temperature of the system.
• When a substance changes state, the potential energy increases and the kinetic energy stays constant.
• The energy required to change the temperature of a substance can be found by Q = m c delta T.
• The energy required to change the state of a substance is Q = m l.
• Specific heat capacity is the amount of energy required to increase the temperature of 1kg of a substance by 1K, without changing its state.
• Specific latent heat is the amount of energy required to change the state of 1kg of a substance, without changing the temperature.
• Specific latent heat of fusion is between a solid and liquid and specific latent heat of vaporisation is between a liquid and a gas.
• Boyle's law is that pressure is inversely proportional to volume.
• Charles' law is that volume is directly proportional to temperature.
• Gay-Lussac's law is that pressure is directly proportional to temperature.
• Absolute zero is 0 k or -273 C and is a theoretical temperature in which particles have no kinetic energy and therefore a gas also has no volume or pressure.
• The ideal gas equation is p V = n R T = N k T.
• Molar mass is the mass in grams of one mole of a substance.
• Brownian motion is the random motion of larger particles in a fluid caused by collisions with surrounding particles, and contributed to the evidence for the existence of atoms and molecules.
• Assumptions in the kinetic theory model include: molecules have no potential energy and therefore there are no intermolecular forces; the duration of collisions is negligible; collisions are perfectly elastic; the motion of the molecules follow Newton's laws and they move in straight lines between collisions.
• Kinetic energy of a single gas molecule can be found by 1/2 m (c rms)^2 = 3/2 k T = (3 R T)/2 N.
• The kinetic theory equation is p V = 1/3 N m (c rms)^2.
• The derivation for the kinetic theory equation is: Consider a cube of side length l with a molecule mass m and velocity u. As it collides with a wall, its change in momentum is 2mu. It must travel 2l to collide with the same wall and so time between collisions t = 2l/u. Force is change of momentum divided by time which is m u^2/l. The pressure is force divided by area which is m u^2/l^3 = m u^2/V. This is all of one particle, the sum of velocities of particles in all directions is 3u = c rms.