Problem

Integrated Concepts (a) Calculate the amount of …

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Problem 75 Hard Difficulty

Integrated Concepts
On its high power setting, a microwave oven produces 900 $\mathrm{W}$ of 2560 $\mathrm{MHz}$ microwaves. (a) How many photons per second is this? (b) How many photons are required to increase the temperature of a $0.500-\mathrm{kg}$ mass of pasta by $45.0^{\circ} \mathrm{C}$ .assuming a specific heat of 0.900 $\mathrm{kcal} / \mathrm{kg} \cdot^{\circ} \mathrm{C}$ ? Neglect all other heat transfer. (c) How long must the microwave operator wait for their pasta to be ready?

Answer

a) $5.30 \times 10^{26}$ photon/s
b) $5.00 \times 10^{28}$
c) 94.2 $\mathrm{s}$

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Physics 103

College Physics for AP® Courses

Chapter 29

Introduction to Quantum Physics

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Video Transcript

and the problem. We're given that a microwave operates at 900 watts, which is our power again. Watts has a unit of jewels per second, which we helpful later. We're also told that it produces the away flings at a frequency of 2560 mega hurts, which is our frequency and mega. We can comfort that to, um hurts leader and part ay asks for how many photons per second is this? So if we are given the power and frequency than we can use our frequency to sulfur the amount of energy that's being produced so we can calculate this with planks constant 6.63 times 10 to the negative, 34 Jules time seconds and a frequency of 2.56 times 10 to the ninth hurts will give us an energy of 1.7 times 10 to the negative 24 jewels. Again, this is how much energy is being produced based on this frequency. So power is equal to energy divided by time, and this energy is the energy of our photons. So if we get our power and divided by energy, then we'll have the number of photons divided by time. So our power we said early, was 900 jewels per second, and we just calculated that our energies 1.7 times 10 to the negative 24 Jules gets us a photons per second of a 5.3 times 10 to the 26 so buttery photons for a second. And then part B asks us to determine. So it's pretty, probie asks this. Determine how many photons are required to increase the temperature of a mass of pasta by 45 degrees Celsius, assuming a specific heat. So for that we could use Hugh equals. Mm. See a Delta T where Q is heat Emma's Mass See a specific heat, which is dependent on the material and delta T is your change in temperature Now our energy or heat will be the number of photons times your energy, so each photon will have this amount of energy, which is the same amount that we calculate earlier. So our heat, which is M. C del city, will be equal to our energy times, our number of photons, so we can actually just use this portion of the equation to solve for and so that gives us em. See, Delta t divided by e were given our mass and kilograms, so that's okay. Is there a 0.5 were given our specific it heat in 0.9 kilo calories per kilogram degrees Celsius. And that's okay because their specific heat, um, can be in those units. So 0.9 he look how and we could make a conversion leader necessary and then 0.9. And then it is telling us that we're changing our changing our temperature by 45 degrees. So that is already are a Delta team again in degree Celsius and that our energy is in one point 697 that we calculated earlier just using the whole number in our calculator times 10 to the negative 24. And again, this is Jules per broton. So that gives us an end value, which is again the number of photons required to increase the temperature as five went zero times Tend toothy 28 Again, this is the number of photons. A. We don't have units for that. And then part see asks us how long Muzzle microwave operator wait for the pasta to be ready again. We have the number of photons required. We have the amount of energy and we have our power. We could go back and solve for our time, the actual amount of time. So, like I said, we solved for our number of photons. We have our power rating. We have our energy and we can use that to solve for tea. So that gives us power equals energy over time and again. Power divided by energy gives us a number of photons divided by tea. And we want to sell for time. So number of photons, times e divided by P gives us our time. And so we can use the numbers. And we previously calculated so five times 10 to the 28th gives us the number of photons we calculate. Earlier, 1.697 times 10 to the negative. 24 jewels was our energy. And our power rating was 900 jewels per second, giving us a time interval off about 94.2 seconds

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