Question

Question 1a : A microwave oven generates 725 W (1 W= 1 J/s) of power. A styrofoam coffee cup has 100.0 grams of water at 22.5 degrees Celsius. If the wavelength of the microwaves is 9.6 cm, how many seconds does it take to make the water boil? The specific heat capacity of water is 4.18 J/g °C. Assume the water retains all heat.

Question 2a : From the previous question, how many photons of microwave radiation are required to make the water boil? Use "E" for scientific notation.

Answer 1

Given that a microwave oven generates 725 W(1W=1J/s) of power.

Mass of water, m = 100 g

Initial temperature, T₁ = 22.5^oC

Boiling temperature of water, T₂ = 100^oC

Heat capacity of water, C = 4.18 J/g^oC

Wavelength of microwaves, λ = 9.6 cm

1a)

Energy per photon is calculated by: E = hυ = hc/λ

E = [(6.65x10^-34J s)x(3.0x10¹⁰cm/s)]/9.6cm = 2.07x10^-24 J/photon

Energy required to heat water, q = mC∆T = (100 g)x(4.18 J/g^oC)x(100-22.5)^oC

q = 32426 J = 3.2426x10⁴J

Time takes to boil water = (1s x3246 J)/725 J = 44.72 s

2a)

Energy per one photon = 2.07x10^-24 J

Number of photons required to boil water = (1photon x32426 J)/ 2.07x10^-24 J

Photons required = 1.566x10²⁸ photons