Question

Infrared lamps are used in restaurents to keep the food warm. The infrared radiation is strongly absorbed by water, raising its temperature and that of the food. If the wavelength of the infrared radiation is assumed to be 1500 nm, then the number of photons per second of infrared radiation produced by an infrared lamp that consumes energy at the rate of 100 W and is 12 % efficient only, is $x\times {10}^{19}$. (Take h = $6\times {10}^{-34}$
x is .

Answer 1

Power of the lamp (rate at which the energy is consumedby the lamp), P = 100 W = 100 J/s
Efficiency = $\frac{lightenergy}{totalenergy}\times 100=12$ %
Amount of infrared light energy absorbed $=12\times 100J\times \frac{1}{100}=12J$
$\Rightarrow nE=12J$
$n\times \frac{hc}{\lambda }=12$
$n=\frac{12\times 1500\times {10}^{-9}}{6.6\times {10}^{-34}\times 3\times {10}^8}=9.09\times {10}^{19}$.