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
(a) To find the rate of power absorption by the spaghetti, we can use the equation:
Power = (mass) x (specific heat) x (change in temperature) / (time)
First, convert the specific heat from kcal/kg·°C to joules/kg·°C:
1 kcal = 4184 J
So, specific heat = 0.900 kcal/kg·°C x 4184 J/kcal = 3765.6 J/kg·°C
Substituting the given values into the equation:
Power = (0.350 kg) x (3765.6 J/kg·°C) x (45.0°C) / (100 s)
Calculating this expression will give you the rate of power absorption by the spaghetti in watts (W).
(b) To find the average intensity of the microwaves, we need to calculate the power delivered to the circular area and then divide it by the area.
The power delivered to the circular area can be calculated using the power formula:
Power = Area x Intensity
Given that the diameter is 20.0 cm, the radius can be found as follows:
Radius = (20.0 cm) / 2 = 10.0 cm = 0.1 m
The area of the circular region is given by the formula for the area of a circle:
Area = π x (radius)^2
Substituting in the values:
Area = π x (0.1 m)^2
Now, rearrange the power formula to solve for intensity:
Intensity = Power / Area
Substitute the known values for Power and Area into the equation, and you will get the average intensity of the microwaves in watts per square meter (W/m^2).
(c) The peak electric field strength of the microwave can be calculated using the equation:
Electric field strength = (Power / Area)^(1/2)
Simply substitute the known values for Power and Area into this equation, and you will get the peak electric field strength in volts per meter (V/m).
(d) The peak magnetic field strength of the microwave can be calculated using the equation:
Magnetic field strength = (Power / (speed of light x Area))^(1/2)
The speed of light, c, is approximately 3.00 x 10^8 m/s.
So, substitute the known values for Power, Area, and c into the equation, and you will get the peak magnetic field strength in teslas (T).