Question

Microwave ovens emit microwave radiation that is absorbed by water. The absorbed radiation is

converted to heat that is transferred to other components of the food. If you have 358.00 ?? of tea (no sugar, no

cream, thank you! I'm on a diet), that absorbs 2.317 × 104 ??? of these microwave photons, increasing its

temperature from 20.00 ℃ to 35.15 ℃, find the wavelength of the microwave photons, in meters.

(???? = 1.091 ?⁄?? ; ?? = 4.184 ?⁄?℃ )

Answer 1

Solution:

Given, Volume of tea = 358 mL

Number of photons = 2.317 × 10⁴ mol

Temperature change (∆T) = 35.15 °C - 20 °C = 15.15 °C

Density of tea = 1.091 g / mL

Specific heat (Cs) = 4.184 J / g °C

We need to calculate Wavelength of photons,

Chemical reactions involve the transfer of heat between system and surroundings. The heat (q) absorbed or evolved is given as:

q = mCs∆T

where, m and Cs are mass and specific heat respectively

∆T is change in temperature

We are given with density and volume of tea. So, we can calculate mass of tea by Density Formula.

We know,   Density = Mass / Volume

Or, Mass = Density × Volume

So, Mass = ( 1.091 g/mL ) × ( 358 mL )

Or, Mass = 390.5 gm

So, the heat absored can be calculated as:

q = ( 390.5 gm ) × ( 4.184 J/g °C ) × ( 15.15 °C )

Or, q = 24852.4 J

We know, Energy of a photon is related to it's Wavelength through Plank's Equation.

According to Plank's Equation,

E = nhc / l

Where, n = number of photons, h = Plank's constant

c = speed of light, l = Wavelength of photon

Or, Wavelength (l) = nhc /E

So, Wavelength(l) = [(2.317 × 10⁴ mol ) × (6.6 × 10^-34 Js) ×(3 × 10⁸ m/s ) ] / [ 24852.4 J ]

Or, Wavelength (l) = 4.58 × 10^-21 m

Hence, Wavelength (l) of photon = 4.58 × 10^-21 m