Suppose that the microwave radiation has a wavelength of 10.8 cm. How many photons are required to heat 215 mL of coffee from 25.0 ^\circ \rm C to 62.0 ^\circ \rm C? Assume that the coffee has the same density, 0.997 g/mL, and specific heat capacity, 4.184 \rm J/(g\cdot K), as water over this temperature range.

Question

Suppose that the microwave radiation has a wavelength of 10.8 cm. How many photons are required to heat 215 mL of coffee from 25.0 ^\circ \rm C to 62.0 ^\circ \rm C? Assume that the coffee has the same density, 0.997 g/mL, and specific heat capacity, 4.184 \rm J/(g\cdot K), as water over this temperature range.

Answer 1

ASSUMING that ^\circ \rm C to be degrees C, then,

E of one photon = hc/wavelength with wavelength in m.
Energy needed to heat the water is
mass H2O x specific heat H2O x (Tfinal-Tinitial).
Set up a ratio and proportion to calculate the number of photons needed. Post your work if you get stuck and please don't use symbols without identifying them.

Answer 2

what is the molarity of the solution if 0.135 g sodium sulfate in total volume of 175mL?

Answer 3

To determine the number of photons required to heat the coffee, we need to follow these steps:

Step 1: Calculate the mass of coffee heated.

The density of coffee is given as 0.997 g/mL. We have 215 mL of coffee, so the mass (m) can be calculated as:

m = volume × density
= 215 mL × 0.997 g/mL

Step 2: Calculate the heat energy required to raise the temperature of the coffee.

The specific heat capacity of coffee (c) was given as 4.184 J/(g·K). We can use the formula Q = mcΔT to calculate the heat energy required, where Q is the heat energy, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.

ΔT = final temperature - initial temperature
= 62.0 °C - 25.0 °C

Now, we can calculate the heat energy (Q) using the formula:

Q = mcΔT

Step 3: Convert the heat energy into the number of photons.

The energy of a single photon can be calculated using the formula E = hc/λ, where E is the energy, h is Planck's constant (6.626 × 10^-34 J·s), c is the speed of light (3.00 × 10^8 m/s), and λ is the wavelength.

First, convert the wavelength from cm to meters:

λ = 10.8 cm × (1 m / 100 cm)

Now, calculate the energy of a single photon using the formula:

E = hc/λ

Finally, divide the heat energy (Q) by the energy of a single photon (E) to find the number of photons required:

Number of photons = Q / E

By following these steps, you will be able to determine the number of photons required to heat the coffee.