Microwave ovens use microwave radiation to heat food. The...

Microwave ovens use microwave radiation to heat food. The energy of the microwaves is absorbed by water molecules in food and then transferred to other components of the food. (a) Suppose that the microwave radiation has a wavelength of 11.2 $\mathrm{cm} .$ How many photons are required to heat 200 $\mathrm{mL}$ of coffee from 23 to $60^{\circ} \mathrm{C} ?(\mathbf{b})$ Suppose the microwave's power is 900 $\mathrm{W}(1$ watt $=1$ joule-second). How long would you have to heat the coffee in part (a)?

Key Concepts

Photon Energy Calculation

This concept involves the quantization of electromagnetic radiation energy using the relation E = hc/?, where E is the energy of a photon, h is Planck's constant, c is the speed of light, and ? is the wavelength of the radiation. It is fundamental in understanding how discrete energy packets (photons) can interact with matter, such as water molecules in food.

Microwave Radiation and Heating Mechanism

Microwave radiation is a form of electromagnetic radiation used in microwave ovens to heat food. The key idea is that microwaves cause polar molecules, like water, to rotate and produce thermal energy through molecular friction, effectively transferring energy uniformly throughout the substance.

Calorimetry and Specific Heat Capacity

This concept involves determining the amount of energy needed to raise the temperature of a given mass of a substance using the specific heat capacity. It underpins the calculation of thermal energy required for heating, using the formula Q = m c ?T, where Q is the energy, m is the mass, c is the specific heat capacity, and ?T is the change in temperature.

Power and Energy-Time Relationship

This concept explains the relationship between power, energy, and time. Power is the rate at which energy is delivered or consumed, expressed as P = Energy/Time. In practical applications such as microwave heating, knowing the power output allows one to calculate the time needed to supply a given amount of energy.

Transcript

00:01 All right.

00:02 So this question told us that we have, ah, microwave that's used to heat up food and the energy of the major with the subject of the water and then transport actually harder.

00:11 A competent of the food.

00:12 And, uh, we told that suppose we have a microwave that has olive lands off by two centimeters and is required to remove it coffee off volume of georgia mule from temperature to interdict recessions.

00:26 The temperature of 60 grew, so she is so we are required to determine the number off legions.

00:34 W quiet.

00:34 You change cause that change in the tone of your off coffee.

00:39 So the first thing we need to do is to the time you ve energy off the ah uh, for, uh, full time and no, the hen and jesu cristo it she'll, verlander.

00:51 And now, because to colombia's long constance is my sister system says by monastery for jewel seconds multiplied by the speed of life, which is three times centers by hatred for sentence divided by the wavelength, which is, uh, 11.2 constants power minus two, because under a centimeter is across the war meter.

01:12 Okay, so this will give others.

01:14 1177 understands by magistrate for joe.

01:18 Okay, now, if we assume that the specifications capacity of what s c.

01:23 S is 4.1, it's job program decree celcius then, uh, can has in that a coffee because coffee is actually bending water makes something...

Please give Ace some feedback