Question

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 1.5 × 10^(-6) m must be absorbed by the water to warm a cup of water (175 g) from 25.0 °C to 40 °C?

a) Number of photons needed
b) Mass of the water
c) Initial temperature
d) Final temperature

Answer 1

To calculate the number of infrared photons needed to warm a cup of water, use the equations N = (Een)/(Ephoton), En = (m)(C)(ΔT), and Ephoton = (hc)/(λ).

Step-by-step explanation:

The number of infrared photons needed to warm a cup of water can be calculated using the equation:

N = (Een)/(Ephoton)

Where N is the number of photons, En is the energy required to heat the water, and Ephoton is the energy of a single photon. The energy required to heat the water can be calculated using the equation:

En = (m)(C)(ΔT)

Where m is the mass of the water, C is the specific heat capacity of water, and ΔT is the change in temperature. The energy of a single photon can be calculated using the equation:

Ephoton = (hc)/(λ)

Where h is Planck's constant, c is the speed of light, and λ is the wavelength of the infrared photon.