(i) Large reflectivity → poor emitter
Explain why a body with large reflectivity is a poor emitter.
When radiation falls on a body, a fraction is reflected, a fraction is absorbed, and (if the body is transparent) a fraction is transmitted. For an opaque body, reflectivity \(R\) and absorptivity \(A\) satisfy:
\[ R + A = 1 \]
- Large reflectivity \(R\) implies small absorptivity \(A\).
- By Kirchhoff’s law of thermal radiation, a good absorber is a good emitter, and a poor absorber is a poor emitter.
Hence, a body with large reflectivity (poor absorber) must be a poor emitter of radiation.
(ii) Brass tumbler vs wooden tray
Explain why a brass tumbler feels much colder than a wooden tray on a chilly day.
- Brass is a good conductor of heat; wood is a poor conductor (insulator).
- When you touch brass, heat flows rapidly from your warm hand to the tumbler, lowering the skin temperature quickly, so it feels very cold.
- Wood conducts heat away very slowly, so your hand does not lose heat quickly and the wooden tray feels relatively warmer, even though both are at the same air temperature.
(iii) Optical pyrometer and red hot iron
Explain why an optical pyrometer calibrated for an ideal black body gives too low a temperature for a red hot iron piece in the open, but a correct value when it is in the furnace.
- An optical pyrometer measures temperature by comparing the brightness (intensity of radiation) of a hot body with that of a calibrated filament, assuming ideal black body behaviour.
- A real red hot iron piece in the open:
- is not a perfect black body (lower emissivity ⇒ dimmer than an ideal black body at the same temperature),
- also suffers from background light and cooling by air.
- Inside the furnace:
- the iron and furnace walls approximate a black body cavity,
- the radiation field is closer to ideal black body radiation with fewer external light interferences.
(iv) Earth without atmosphere → very cold
Explain why the earth without its atmosphere would be inhospitably cold.
- The atmosphere (especially water vapour, carbon dioxide, etc.) causes the greenhouse effect:
- It is largely transparent to incoming solar radiation (short wavelength).
- It absorbs and partly re-radiates the outgoing infrared radiation from the Earth back to the surface.
- Without the atmosphere, the Earth would radiate heat directly into space with no “blanket” to trap part of it. The average surface temperature would drop far below the present value, making conditions inhospitably cold.
(v) Steam heating vs hot water heating
Explain why heating systems based on circulation of steam are more efficient than those based on circulation of hot water.
- Steam at \(100^\circ\text{C}\) carries a large amount of latent heat of vaporization in addition to its sensible heat.
- When steam condenses to water in the radiators/pipes inside a building, it releases this large latent heat: \[ Q = mL \] where \(L\) is very large for water.
- Thus, for the same mass and temperature range, steam can deliver much more heat energy than hot water, making steam-based systems more efficient and quicker in warming a building.