Microwave ovens emit microwave radiation that is absorbed by water as heat. Suppose that the wavelength of the radiation that is 12.5 cm in an oven that has a power rating of 900 watts. (1W = 1 J/s)
a) How many moles of photons are released per minute
b) how long will it take to heat 100m.L of water from 20 Celsius to 100 Celsius. Assume all the water gets all of the microwaves energy as heat.
energy in J = hc/wavelength.That is E in J for 1 photon. Multiply by 6.022E23 to find moles. How many seconds will it take to at 900 watts. Multiply by 60 seconds/min.
Energy needed to heat water is
mass water x specific heat water x (Tfinal-Tinitial) = q.
A typical laser pointer is rated at 5.0 mW. It outputs red light with a wavelength of about 6300 Angstrom. How many photons of laser light will be emitted from the pointer if it is used 120 seconds.
To answer these questions, we need to understand the relationship between power, energy, and time, as well as the energy of each photon.
a) The power rating of the oven, given as 900 watts, tells us that the oven emits 900 joules of energy per second. We need to find out how many photons are released per minute.
First, let's find the energy of each photon. We can use the equation:
Energy (E) = Planck's constant (h) × speed of light (c) / wavelength (λ)
Since the wavelength is given in centimeters, we need to convert it to meters.
Given: wavelength = 12.5 cm = 0.125 m
Now, let's calculate the energy of each photon. The value of Planck's constant (h) is approximately 6.63 × 10^(-34) J·s, and the speed of light (c) is 3 × 10^8 m/s.
Energy (E) = (6.63 × 10^(-34) J·s × 3 × 10^8 m/s) / (0.125 m)
Simplifying the equation:
E = 1.59 × 10^(-25) J
Now, let's calculate how many photons are released per second by dividing the oven's power (900 W) by the energy of each photon (1.59 × 10^(-25) J):
Number of photons per second = Power (Watts) / Energy of each photon (J)
Number of photons per second = 900 W / 1.59 × 10^(-25) J
Number of photons per second ≈ 5.66 × 10^26 photons
To find the number of photons released per minute, we can multiply the above result by 60 seconds:
Number of photons per minute ≈ (5.66 × 10^26 photons/s) × 60 s
Number of photons per minute ≈ 3.40 × 10^28 photons
Therefore, approximately 3.40 × 10^28 moles of photons are released per minute.
b) To calculate the time required to heat 100 mL of water from 20°C to 100°C using the energy from the microwave oven, we can follow these steps:
1. Find the mass of water in grams:
Given: volume = 100 mL = 100 g (since the density of water is approximately 1 g/mL)
2. Determine the heat required to raise the temperature of the water:
Heat (Q) = mass (g) × specific heat capacity (c) × temperature change (ΔT)
The specific heat capacity of water is approximately 4.184 J/(g·°C).
Using the equation, Q = 100 g × 4.184 J/(g·°C) × (100°C - 20°C):
Q ≈ 3.35 × 10^4 J
3. Divide the total energy (3.35 × 10^4 J) by the power output of the microwave oven (900 W) to find the time required:
Time (minutes) = Total energy (J) / Power (W) / 60
Time ≈ (3.35 × 10^4 J) / (900 W) / 60
Time ≈ 6.21 minutes
Therefore, it will take approximately 6.21 minutes to heat 100 mL of water from 20°C to 100°C using all the microwave oven's energy.