Question

Water is exposed to infrared radiation of wavelength 2.6×10−4 cm . How many photons will be required to raise the temperature of 2.1 g of water by 2.3 K ?

Answer 1

Specific heat capacity of water = 4.184 J/g. K

Thus energy required to raise the temperature of water by 2.3 K = 2.3 x 4.184 x 2.1 = 20.2 J

(note: specific heat capacity is the energy required to raise the temperature by 1K of a 1g substance )

Energy of a photon = hc/wavelength

h = 6.626 x 10^-34 J.s, c = 3x 10⁸ m/s, wavelength =2.6 x 10^-6 m (wavelength has been converted to m)

on substituting these values

energy of one photon = 6.626 x 10^-34 . 3x 10⁸ / 2.6 x 10^-6 = 0.76 x 10^-19 J

Number of photons required to produce 20.2 J = 20.2/0.76 x 10^-19 = 26.57 x 10¹⁹ photons