Photons of infrared radiation are responsible for much of the warmth we feel when holding our hands before a fire. These photons will also warm other objects. How many infrared photons with a wavelength of 1.5x10^-6 m must be absorbed by the water to warm a cup of water (175g) from 25.0°C to 40°C

The number of photons required is .

The total energy required to raise the temperature of water from 25.0°C to 40°C will be provided by the energy carried by the photons.

The energy required to raise the temperature of water from 25.0°C to 40°C will be:

ΔQ = mcΔT

where, m = mass of water = 175 g (given)

            c = specific heat capacity of water = 4.186 J/g°C

            ΔT = change in temperature = 40 - 25 = 15°C

ΔQ = 175 × 4.186 × 15 = 10988.25 J

So the photos must provide ΔQ amount of energy.

The energy carried by one photon:

E = hc/λ

where, h = Planck's constant, c = speed of light and λ = wavelength of photon = m

=

No of photons needed to produce ΔQ amount of energy:

n = ΔQ / E =

n = , is the number of photons required.

Learn more about Infrared Radiation:

link

photons

Explanation:

The energy of a photon is given by

where

is the Planck constant

is the speed of light

is the photon wavelength

Here we have

So, the energy of 1 of these infrared photons is

The amount of energy needed to increase the temperature of the cup of water is:

where

m = 175 g is the mass

is the specific heat capacity

is the increase in temperature

So,

Therefore, the number of photons needed is:

6.4 cm (max) - 25 cm (min)