(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Estimate

(i) the mass of the brakes of a train needed to stop the brake block temperature reaching melting point when the brakes are applied

(ii) the number of photons emitted per second by a light bulb

An order of magnitude estimate is sufficient.

2. Relevant equations

3. The attempt at a solution

For i),

I assumed that all of the kinetic energy of the train is converted to thermal kinetic energy of the material.

The thermal energy is on the order of kT.

I assumed that the speed of the train is 30 m/s and that the mass of the train is 2000 kg.

So, kT = 0.5mv^{2}

This gives T = 3.2*10^{30}K.

This is clearly absurd!!!!!

For ii),

power of a typical light bulb = I^{2}R = (50 mA)^{2}(1.5 ohms) = 380 mW.

And energy of one light photon = hc/lamba = 2.9*10^{-17}J.

(assuming lamba = 700 nm).

So, number of photons = power of light bulb / energy of one photon = 1.3*10^{12}s^{-1},

which is a sensible number.

I'd be grateful to you to anyone who suggests a much better way.

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# Homework Help: Conversion of work to heat: Getting the Sun's temperature inside a braking block!

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