On its highest power setting, a microwave oven increases the temperature of 0.350 kg of spaghetti by 45.0°C in 100 s.
(a) What was the rate of power absorption by the spaghetti, given its specific heat is 0.900 kcal/kg·°C?
W
(b) Find the average intensity of the microwaves, given they are absorbed over a circular area 20.0 cm in diameter.
W/m2
(c) What is the peak electric field strength of the microwave?
V/m
(d) What is its peak magnetic field strength?
T
To get the solution to this question, we will need to use equations relating to power, specific heat, intensity, and electric and magnetic fields. Let's take it step by step.
(a) To calculate the rate of power absorption by the spaghetti, we can use the formula:
Power = (mass) x (specific heat) x (temperature change) / (time)
Given:
mass = 0.350 kg
specific heat = 0.900 kcal/kg·°C
temperature change = 45.0°C
time = 100 s
Using these values, we can plug them into the formula to find the rate of power absorption:
Power = (0.350 kg) x (0.900 kcal/kg·°C) x (45.0°C) / (100 s)
Calculating this gives us the power absorption rate:
Power = 0.14175 kcal/s
To convert kcal/s to watts, we need to multiply the result by 4.186 (since 1 kcal/s = 4.186 W).
Power = (0.14175 kcal/s) x (4.186 W/kcal/s)
Calculating this final conversion gives us the rate of power absorption by the spaghetti:
Power = 0.592 W
Therefore, the rate of power absorption by the spaghetti is 0.592 W.
(b) To find the average intensity of the microwaves, we can use the formula:
Intensity = Power / (area)
Given:
diameter of the circular area = 20.0 cm
First, we need to calculate the radius of the circular area:
radius = diameter / 2 = 20.0 cm / 2 = 10.0 cm = 0.10 m
Next, we need to find the area of the circular area using the formula:
area = π x (radius^2)
Plugging in the values, we get:
area = π x (0.10 m)^2
Calculating this gives us the area:
area = 0.0314 m^2
Now, we can plug the power and area values into the formula to find the average intensity of the microwaves:
Intensity = 0.592 W / 0.0314 m^2
Calculating this gives us the average intensity of the microwaves:
Intensity = 18.85 W/m^2
Therefore, the average intensity of the microwaves is 18.85 W/m^2.
(c) To calculate the peak electric field strength of the microwave, we can use the formula:
Electric field strength = √(2 x Intensity / (speed of light))
Given:
Intensity = 18.85 W/m^2
Speed of light = 3.00 x 10^8 m/s
Plugging in the values, we get:
Electric field strength = √(2 x 18.85 W/m^2 / (3.00 x 10^8 m/s))
Calculating this gives us the peak electric field strength of the microwave:
Electric field strength = 6.82 x 10^-4 V/m
Therefore, the peak electric field strength of the microwave is 6.82 x 10^-4 V/m.
(d) To find the peak magnetic field strength, we can use the formula:
Magnetic field strength = Electric field strength / (speed of light)
Given:
Electric field strength = 6.82 x 10^-4 V/m
Speed of light = 3.00 x 10^8 m/s
Plugging in the values, we get:
Magnetic field strength = 6.82 x 10^-4 V/m / (3.00 x 10^8 m/s)
Calculating this gives us the peak magnetic field strength:
Magnetic field strength = 2.27 x 10^-12 T
Therefore, the peak magnetic field strength of the microwave is 2.27 x 10^-12 T.