Romania Clasa a X-a Physics
Chapters: 3
1. Elements of thermodynamics
Basic thermodynamic ideas · Calorimetry · First law of thermodynamics · Changes of state · Heat engines · Second law of thermodynamics
- Thermodynamic Processes: Isothermal, Adiabatic and More – A thermodynamic process takes a gas from one state to another; on a P–V graph it is a path. Isothermal: T fixed, PV = constant, W = nRT ln(V₂/V₁), ΔU = 0. Adiabatic: no heat in or out, PV^γ = constant, W = nR(T₁ − T₂)/(γ − 1), the gas cools when it expands. Isobaric: P fixed, W = PΔV. Isochoric: V fixed, W = 0. Reversible processes go slowly through equilibrium states; real, fast ones are irreversible. In a cyclic process the gas returns to its start, ΔU = 0 and net work = area of the loop.
- Thermal Expansion, Specific Heat, Calorimetry and Latent Heat – Temperature tells how hot a body is; heat is energy that flows because of a temperature difference. Most things expand when heated: ΔL = αLΔT, ΔA = βAΔT, ΔV = γVΔT, with β = 2α and γ = 3α. Water is an exception between 0 °C and 4 °C, where it shrinks on heating, so it is densest at 4 °C. The heat needed to warm a body is Q = mcΔT, where c is the specific heat; gases have two, Cp > Cv, with Cp − Cv = R per mole. In calorimetry, heat lost by hot bodies equals heat gained by cold ones. During melting or boiling the temperature stays constant and heat Q = mL goes into changing the state.
- First Law of Thermodynamics – Internal energy U is the total energy of the molecules inside a system. It changes in only two ways: by heat Q (energy that flows because of a temperature difference) and by work W (energy moved by a force, like a moving piston). First law: ΔQ = ΔU + ΔW. Heat given to a gas partly raises its internal energy and partly lets it do work. Work by a gas at constant pressure is PΔV. For an ideal gas Cp − Cv = R.
- Phase Changes: Latent Heat, Vapour Pressure and Phase Diagrams – A phase change is when matter moves between solid, liquid and gas. During a change the temperature stays the same; the heat used is latent heat (Q = m × L). A liquid boils when its vapour pressure equals the pressure above it, so boiling point falls with lower pressure. A phase diagram maps the state at every temperature and pressure; its lines meet at the triple point and the liquid–gas line ends at the critical point.
- Second Law of Thermodynamics, Heat Engines and Refrigerators – The first law says energy is conserved; the second law says which way heat and energy can go. Heat flows by itself only from hot to cold (Clausius). No engine can turn all the heat it takes into work; some must be thrown into a colder body (Kelvin–Planck). A heat engine takes Q₁ from a hot source, does work W and rejects Q₂: efficiency η = W/Q₁ = 1 − Q₂/Q₁. A refrigerator uses work W to move Q₂ from cold to hot: COP α = Q₂/W. The best possible engine, the Carnot engine, has η = 1 − T₂/T₁.
2. Producing and using direct current
Electric current · Ohm's law · Kirchhoff's laws · Combining resistors and sources · Electric energy and power · Effects of current and applications
- Current in a Metal: Drift Velocity and Mobility – In a metal, free electrons move very fast in random directions, so on average they go nowhere. An electric field adds a small, steady shift opposite to the field: the drift velocity vd = eEτ/m. The current is I = n e A vd, and the current density is j = n e vd. Mobility μ = vd/E tells how easily a charge drifts. Drift speed is only about a millimetre per second, yet a bulb lights at once because the field is set up in the whole wire almost instantly.
- Ohm's Law, Resistivity and Effect of Temperature – Using drift velocity, V = IR with R = ml/(ne²τA) = ρl/A. Resistivity ρ = m/(ne²τ) depends only on the material and temperature; conductivity σ = 1/ρ. Ohm's law in vector form is j = σE. Metals, wires and resistors give a straight V–I line (ohmic); bulbs, diodes and devices like GaAs give curved or one-way graphs (non-ohmic). For metals ρ rises with temperature: ρT = ρ0[1 + α(T − T0)]; alloys like nichrome change very little; semiconductors get lower ρ when hot.
- Kirchhoff's Rules and the Wheatstone Bridge – Junction rule: at any junction, the sum of currents entering equals the sum leaving (ΣI = 0), because charge is conserved. Loop rule: around any closed loop, the algebraic sum of potential changes is zero (ΣΔV = 0), because energy is conserved. Sign rules: a resistor crossed along the current gives −IR; a cell crossed from − to + gives +ε. A Wheatstone bridge of four resistors P, Q, R, S is balanced (no galvanometer current) when P/Q = R/S; this lets us find an unknown resistance, as in the metre bridge.
- Resistors in Series and Parallel – In series, resistors form one path: the same current flows through each, voltages add up and R_s = R₁ + R₂ + R₃. In parallel, each resistor gets its own branch: the voltage across each is the same, currents add up and 1/R_p = 1/R₁ + 1/R₂ + 1/R₃, so R_p is smaller than the smallest resistor.
- Electric Power and Electrical Energy – Electric power is the rate of using electrical energy: P = VI = I²R = V²/R, in watts. Energy used = power × time. At home energy is measured in kilowatt-hours: 1 kWh = 1 unit = 3.6 × 10⁶ J. Bill = units × rate.
- Heating Effect of Electric Current – When current flows through a resistor, electrical energy turns into heat. Joule's law: H = I²Rt, so heat grows with the square of current, with resistance and with time. Heaters, irons, toasters, bulbs and fuses all use this effect.
3. Producing and using alternating current
Alternating current · Circuit elements in AC · Energy and power in AC · Transformer · Electric motors and appliances
- Alternating Current – An alternating current (AC) changes size and direction again and again: I = I₀ sin ωt. Its rms value is I₀/√2, the steady DC that gives the same heating. A resistor keeps V and I in step; an inductor makes I lag by 90° (Xʟ = ωL); a capacitor makes I lead by 90° (Xᴄ = 1/ωC). In a series LCR circuit Z = √(R² + (Xʟ − Xᴄ)²), resonance happens when Xʟ = Xᴄ, and average power is P = Vrms Irms cos φ.
- Force on a Current-Carrying Conductor, Motor and Induction – A wire carrying current inside a magnetic field feels a push. The push is biggest when the wire is at 90° to the field and zero when it is parallel. Fleming's left-hand rule gives its direction. A motor uses this push to spin a coil; a generator does the reverse and makes current by moving a coil or magnet.
- AC Generator and Transformer – An AC generator turns a coil in a magnetic field. The flux through it keeps changing, so it makes an emf e = NBAω sin ωt with peak NBAω. A transformer uses mutual induction between two coils on one iron core: Vs/Vp = Ns/Np. A step-up transformer raises voltage and lowers current; a step-down does the opposite. Power stays nearly the same (Vp Ip ≈ Vs Is).