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- A close analogy exists between the flow of energy by heat because of a temperature difference (see Section 19.6) and the flow of electric charge because of a potential difference. In a metal, energy dQ and electrical charge dq are both transported by free electrons. Consequently, a good electri- cal conductor is usually a good thermal conductor as well. Consider a thin conducting slab of thickness dx, area A, and electrical conductivity ơ, with a potential difference dV between opposite faces. (a) Show that the current I = dq/dt is given by the equation on the left: Charge conduction Thermal conduction dq = oA dt dT kA dt dQ AP dx dx In the analogous thermal conduction equation on the right (Eq. 19.17), the rate dQ/dt of energy flow by heat (in SI units of joules per second) is due to a temperature gradient dT/dx in a material of thermal conductivity k. (b) State anal- ogous rules relating the direction of the electric current to the change in potential and relating the direction of…A close analogy exists between the flow of energy by heat because of a temperature difference (see Section 20.7) and the flow of electric charge because of a potential difference. In a metal, energy dQ and electrical charge dq are both transported by free electrons. Consequently, a good electrical conductor is usually a good thermal conductor as well. Consider a thin conducting slab of thickness dx, area A, and electrical conductivity o, with a potential difference dv between opposite faces. (a) Show that the current I = dq/dt is given by the equation on the left: Charge conduction Thermal conduction dq TA dt JdT| kA dt dQ | dx |AP| |dx In the analogous thermal conduction equation on the right (Eq. 20.15), the rate dQ/dt of energy flow by heat (in Sl units of joules per second) is due to a temperature gradient dT/dx in a material of thermal conductivity k. (b) State analogous rules relating the direction of the electric current to the change in potential and relating the direction of…按ESC | 即可退出全屏模式 Gas insulation is important for transmission lines, outdoor insulators and Gas-insulated- Substations (GIS). Understanding the breakdown mechanisms and behaviour of insulation materials is key to the optimum design of insulation systems. The speed distribution function of electrons in a gas containing electrons, ions and atoms is controlled by the electric field strength, E, and can be expressed as fo (E, v). It satisfies the relationship of (E, v) dv=1. i) ii) Convert the above electron speed distribution function into an electron energy distribution function that satisfies the relationship f(E, ɛ) dɛ =1 where & is the electron energy and ƒ(E, ɛ) the electron energy distribution function. The electron number density is ne and the atom number density is na in the gas. The ionisation cross section of the atoms by electron impact is a function of electron energy, ɛ, and can be written as σ¡ (ɛ). Similarly, the attachment collision cross section between an electron and an…
- Suppose you have an antique copper penny in your pocket. Modeling the conduction electrons in the penny as an ideal gas, use results from Chapter 20 to estimate their kinetic energy and root-mean-square (rms) velocity. (Assume that the temperature is 27.1°C.) kinetic energy J rms m/sif the heat capacitance for a Container of Aluminum is 270 J/Co and the specific tempreture of Aluminum is 900 J/kg.Co , find the Container massElectrons flow through a 3.0-mm-diameter aluminum wire at 1.8×10−4 m/s. How many electrons move through a cross section of the wire each day?
- A solid conduetor of eireular eross-setion with a radius of 5 mm has a conductivity that varies with radins. The conductor is 20 m long and there is a potentinl difference of 0.1 V de between its two ends. Within the conductor, II –- 10°p²a, A/m. Find J as a funetion of gA close analogy exists between the flow of energy by heat because of a temperature difference (see Section 19.6) and the flow of electric charge because of a potential difference. In a metal, energy dQ and electrical charge dq are both transported by free electrons. Consequently, a good electrical conductor is usually a good thermal conductor as well. Consider a thin conducting slab of thickness dx, area A, and electrical conductivity , with a potential difference dV between opposite faces. (a) Show that the current I = dq/dt is given by the equation on the left: ChargeconductionThermalconductiondqdt=A|dVdx|dQdt=kA|dTdx| In the analogous thermal conduction equation on the right (Eq. 19.17), the rate dQ/dt of energy flow by heat (in SI units of joules per second) is due to a temperature gradient dT/dx in a material of thermal conductivity k. (b) State analogous rules relating the direction of the electric current to the change in potential and relating the direction of energy flow to the change in temperature.Rubbing a balloon in your hair it will make it stick to the wall of your room for various length of time. (a) How the balloon stick? (b) Explain why this experiment is more successful in the winter than during the summer. (c) If you were to rub a balloon in your hair and try to stick it to a metal can, would the balloon stick? Explain.
- Copper wire has a resistivity ρ = 1.7 × 10-8 Ω⋅m when at 20°C and it has a temperature coefficient α = 3.9 × 10-3 K-1. A solid cylinder of copper of length L = 85 cm and diameter D = 3.5 mm has one end held at T1 = 14°C and the other end is held at T2 = 210°C. The temperature increases linearly between the two ends of the cylinder. 1A) Consider a thin slice of the copper cylinder of thickness dx that is located a distance x from the left end of the cylinder. Write an equation for the temperature of this slice in terms of the variables x, L, T1, and T2. The answer to part a is T=( x/L ) T2 + ( 1 - ( x/L ) ) T1 b) Determine the total resistance in milliohms.Copper wire has a resistivity ρ = 1.7 × 10-8 Ω⋅m when at 20°C and it has a temperature coefficient α = 3.9 × 10-3 K-1. A solid cylinder of copper of length L = 85 cm and diameter D = 3.5 mm has one end held at T1 = 14°C and the other end is held at T2 = 210°C. The temperature increases linearly between the two ends of the cylinder. A) Consider a thin slice of the copper cylinder of thickness dx that is located a distance x from the left end of the cylinder. Write an equation for the temperature of this slice in terms of the variables x, L, T1, and T2. B) Determine the total resistance in milliohms.Copper wire has a resistivity ρ = 1.7 × 10-8 Ω⋅m when at 20°C and it has a temperature coefficient α = 3.9 × 10-3 K-1. A solid cylinder of copper of length L = 85 cm and diameter D = 3.5 mm has one end held at T1 = 14°C and the other end is held at T2 = 210°C. The temperature increases linearly between the two ends of the cylinder. 1a) Consider a thin slice of the copper cylinder of thickness dx that is located a distance x from the left end of the cylinder. Write an equation for the temperature of this slice in terms of the variables x, L, T1, and T2. 2a) Determine the total resistance in milliohms.