PHYS213 Final Exam - Cheat Sheet LAST VERSION

# PHYS213 Final Exam - Cheat Sheet LAST VERSION - Water max...

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Water: max ρ at 4°C. above 4° expands when heated until 100°C. below 4°C expands when cooled until 0°C. Internal E : E of system when it is stationary – nuclear, chemical, strain, etc. Thermal E : energy that changes when the T changes, associated w/ motions of atoms, molecules, etc. Cal: 1g water 14.5 → 15.5 °C. BTU: 1 lb water 63 → 64°F. SI: Joule. 1 cal = 4.186 J. Work done during V change : Gas cylinder piston cylinder area A, gas pressure p, gas volume V. Gas expands, piston moves by ds, volume changes to V + dV = V + A ds. Work done BY the gas: dW = p dV. Work done by the gas during the V change from Vi to Vf is [integral Vi to Vf] p dV. P-V diagram : W = [integral Vi to Vf] p dV. Area under the curve is work. Closed cycle: net W = enclosed area. Same Vi and Vf but different paths lead to different areas/different work. 1 st law: heat added to the system – work done by the system: ΔE = Q-W. Sign of work done on the system would be opposite. Heat transfer mechanisms: Conduction = through the materials (exchange of kinetic energy between molecules or atoms of insulators or free electrons of metals), convection = through the movement of a heated substance (natural – results from difference in density, forced = heated substance forced to move), Radiation = through emission of EM ±eld. Assumptions of ideal gas: large # molecules, avg separation btw molecules large, molecules move randomly, molecules obey Newton’s law, molecules collide elastically w/ each other and container, molecules are identical. Pressure = F/A, F = dp/dt – rate of momentum given to surface by collisions. Pressure → density x kinetic energy; T → kinetic energy Mean free path: decreases w/ bigger molecules or more molecules (both → more collisions) Equipartition of energy: every kind of molecule has a certain num- ber f of degrees of freedom, which are independent ways in which the molecule can store energy. Each df can store on avg 0.5kT of energy per molecule (0.5RT per mol). Translational: molecules moving in axis system as a unit. Rotational: spinning around axis like a top. Vibrational: only at high T. Heat engine is a device that carries a working substance thru a cyclic process during which it (a) absorbs thermal E from a high-T source (b) does work (c) expels thermal E to a low-T source. Refrigerator is a heat engine in reverse.

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It carries a working substance thru a cyclic process during which it (a) absorbs thermal E from a low-T source (b) work is done on it (c) expels energy to a high-T source Reversible process: at its conclusion, the system and its sur- roundings return to the exact intital conditions. All natural processes are at best “almost” reversible. Carnot engine: heat engine operating in a Carnot cycle (four reversible processes: two adiabatic (bc,da), two isothermal (ab,cd)) – most efFcient heat engine possible Impossible to construct heat engine with 100% efFciency or refrigerator which does not require work Entropy: state
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PHYS213 Final Exam - Cheat Sheet LAST VERSION - Water max...

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