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Applied Physics. Contents. Rotational Dynamics Thermodynamics & Engines. Rotational Dynamics. Angular velocity : the angle of a circle (arc) mapped out by a rotating object per second: ω = θ s -1 Angular displacement : θ Angular velocity : ω = θ t -1

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## Applied Physics

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**Contents**• Rotational Dynamics • Thermodynamics & Engines**Rotational Dynamics**• Angular velocity: the angle of a circle (arc) mapped out by a rotating object per second: ω = θs-1 • Angular displacement: θ • Angular velocity: ω = θt-1 • Angular acceleration: α = Δω/Δt**Rotational Dynamics**• Moment of Inertia: Inertia = objects have a degree of reluctance to move. Moment of inertia is this but in rotational movement. Objects oppose the movement of angular acceleration. The more they oppose, the greater the moment of inertia (kgm2) • Circular disc: I = Mr2/2 • Solid cylinder: I = Mr2 • Solid sphere: I = 2Mr2/5 • Kinetic Energy: EK = ½Iω2**Rotational Dynamics**• Torque: Turning force • Pulling force causes torque, T: T = Fr • In terms of inertia: T = Iα**Rotational Momentum & Power**• Angular Momentum, (L): momentum = mass x velocity. Angular momentum occurs in rotational movement L (kgm2s-1) = Iω angular momentum before = angular momentum after • Impulse: change in momentum • Angular Impulse, ΔL: change in angular momentum ΔL = TΔt (small torque for long duration = large torque for small duration)**Rotational Momentum & Power**• Work & Power: • Work done = force x perpendicular distance… so… • Work done = torque x angle rotated W = Tθ • Power = force x speed… so… • Power = torque x angular velocity P = Tω**1st Law of Thermodynamics**• 1st Law of Thermodynamics: Energy can be neither created nor destroyed (conservation of energy) - Thus power generation processes and energy sources actually involve conversion of energy from one form to another, rather than creation of energy from nothing ΔQ = ΔU + ΔW ΔU: Change in internal energy of the system ΔQ: Heat transferred into/out of the system ΔW: Work done by/on the system**1st Law of Thermodynamics**• Cylinder has area, A. A fluid is admitted at constant pressure, p p = F/A & Wd = fd … rearrange: F = pA Wd = pAd (Ad = volume, V) Wd = pV or ΔWd = pΔV**1st Law of Thermodynamics**• pV = nRT (Ideal Gas Law) • Boyle’s Law: pV = constant - Temperature remains constant (isothermal) - pV = constant and p1V1 = p2V2 - ΔU = 0 because the internal energy is dependent on temperature, which does not change - ΔQ = ΔW. If the gas expands to do work ΔW, & amount of heat ΔQ must be supplied - compression or expansion produces the same graph**1st Law of Thermodynamics**• Adiabatic: no heat flow (ΔQ=0) into or out of a system • For a change in pressure or volume in a system, the temperature loss can be calculated: p1V1/T1 = p2V2/T2 • At high p, low V: adiabatic = value expected for isothermal at high T • At low p, high V: adiabatic cuts isothermal at low T • Equation for adiabatic line: pVγ = k γ = Cp/Cv k = constant Adiabatic compression**1st Law of Thermodynamics**• Isovolumetric: p1T1 = p2T2 • Isobaric: V1T1 = V2T2 Adiabatic compression**P-V diagrams & Engines**• Gases undergo changes that will eventually cause them to return to the original state. An ideal gas undergoing these changes has the properties shown below: - Isovolumetric changes between a & b and c & d - Isobaric changes between b & c and d & a**P-V diagrams & Engines**• Thermal Efficiency: net work output ÷ heat input • Actual efficiency of the engine will be lower than the value of thermal efficiency alone, due to frictional losses within the engine. The efficiency of a car = approx. 30% • Petrol Engine: Otto Cycle**P-V diagrams & Engines**• Diesel Engine: - Higher thermal efficiency that petrol engines - Heavier than petrol engines - More noise and incomplete combustion (pollution) • Both Engines: power output: area of p-V loop x no cylinders x no cycles per sec maximum energy input: fuel calorific value x fuel flow rate**2nd Law & Engines**• 2nd Law of Thermodynamics: Entropy of an isolated system not in equilibrium will tend to increase over time, approaching a maximum value at equilibrium - i.e. entropy increases & all processes tend towards chaos • Temperature gradient: Heat flows from a region of hot temperature to a region of cold temperature • All heat engines give up their energy to a cold reservoir Qin:heat flow from the hot reservoir to the engine • Qout: heat flow from the engine to the cold reservoir. • Work done by heat engine = Qin – Qout Efficiency = W/Qin = (Qin – Qout)/Qin**2nd Law & Engines**• Limitations to Thermal Efficiency: - in an engine: • TH cannot be too high components could melt • TC will be in the range of atmospheric temperatures • Analysis of the engine cycle can help to improve efficiency • Design of ports so that gas can get enter & exit with min. resistance • Lubrication reduces friction in bearings Therefore an engine will never work at its theoretical efficiency**Summary**• Rotational Dynamics • Rotational Momentum & Power • 1st Law of Thermodynamics • P-V diagrams & Engines • 2nd Law & Engines

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