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(a) By what factor does the peak frequency change if the Kelvin temperature of an object is doubled from 20.0 $\mathrm{K}$ to 40.0 $\mathrm{K}$ ? (b) Bywhat factor does the peak frequency change if the Celsius temperature of an object is doubled from $20.0^{\circ} \mathrm{C}$ to $40.0^{\circ} \mathrm{C}$ ?

a) 2b) 0.97

Physics 103

Chapter 30

Quantum Physics

Rutgers, The State University of New Jersey

University of Washington

Simon Fraser University

University of Sheffield

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beak frequency equals 5.8. It multiply by 10 to the power 10 times. D, Huh? So peak frequency equals five point 88 month supply by 10 to the power, then multiply by t. Uh, he's the absolute temperature. Um, you the equals to t uh, temperature is doubled. Ah, let's say temporary Initial temperature is ah 20 Calvin's and this temperature is increased toe 40 Calvin's If Calvin temperature is doubled, what happens to the peak frequency? Um, let's see. Now let's put t is equal to duty in this equation. Um, and the new frequencies if prime beak equals five point, I hate it. Multiply by 10 to the power, then multiplied by duty because, ah, temperature eyes increased from 20 calving to 40. Cal win, so temperature is doubled. Therefore, resect the substitute. He's equal to two tea on Ben solving this we have 5.88 multiplied by 10 to the power, then multiply by Do and then we have ah to as well. And now this, uh, can be returnees if Brian Beak equals yeah, beak multiply by two and the ratio between if Brian Beak and F beak equals two, which means that if temperature is, if Calvin temperature is increased from 20 calories into 40 Calvin, then a peak frequency increases by a factor off too. So, big frequency, um, secret Quincy speak frequency increases increases by ahh factor. Do. If a Calvin temperature is double, it increases from 20 Kalyan to 40 calories. All right, now, let's do part. Be in part B. We have speak frequency F beak equals five point 88 Multiply by 10 to the power, then times D. In this case, D equals 20 degree Celsius. 20 degrees Celsius equals 2 93 Calvin and therefore beak frequency equals five point it. It multiplied by 10 to the power, then multiplied by do 93. Also, we have d'oh prime equals 40 degree centigrade. A temperature is increased from 20 degree centigrade to 40 degrees centigrade. Um, let's say final temperature is D prime. And, uh, the new frequency is let's say if rhyme beak. If Brian Beak equals 5.88 multiply by 10 to the power 10 multiplied by T prime to pry Michel's 40 degrees centigrade and it's 40 degrees centigrade equals, um, 313 313 cabins. And therefore, if Brian Peak, If Brian Beak equals 5.88 multiplied by 10 to the power, then multiply by T Prime, which is 313 Calvin. Now let's find out the ratio. If Brian Beak divided by F Peak F beak, equals five point 88 multiply by 10 to the power, then multiply by 313. Divided by F. Beak is 5.8. It multiply by 10 to the power 10. Multiply by to 93. 5.80 gets cancelled. Ah, but 5.8 it 10 to the power then as well. And we're only left with If Crime Week, divided by F beak, equals 314 divided by 2 93 and dividing the two numbers, we get 1.0 six eat

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