Temperature change in bottle?

You put a bottle of soft drink in a refrigerator and leave it until its temperature has dropped 20.0 K.



What is its temperature change in degrees Fahrenheit?



What is its temperature change in degrees Celsius?



I know how to do the conversions, and I even did the conversions using google and the answers are incorrect apparently. I got -423.67 for the first question and -253.15 for the second but they're incorrect answers apparently. Please help.Temperature change in bottle?
I think your problem is that you're converting 20 K into an actual temperature, instead of a temperature change. The question is concerned with the size of a degree on each scale.



Think about the problem this way. Start out with a soda at 280 K. You put it in the fridge and the temperature drops 20 K to 260 K.



In order to find the temperature change in Celsius, you would convert 280 K and 260 K to 掳C, and find the difference.



280 K = 7 掳C

260 K = -13 掳C



Change in temperature:



260 K - 280 K = -13 掳C - 7 掳C = -20 掳C



Same with Fahrenheit



280 K = 44.33 掳F

260 K = 8.33 掳F



Change in temperature:



260 K - 280 K = 8.33 掳F - 44.33 掳F = -36 掳C



Let's do that symbolically. For change in Kelvin to change in Celsius, we start with the conversion from Kelvin to Celsius.



K = C + 273



So, if we've got temperature 1 in Kelvin (K1) and Celsius (C1) and temperature 2 in Kelvin (K2) and Celsius (C2), then the difference between them is



K2 - K1 = (C2 + 273) - (C1 + 273)

K2 - K1 = C2 + 273 - C1 - 273

K2 - K1 = C2 - C1



So a degree change in Kelvin is equal to a degree change in Celsius. This makes sense, because the Kelvin scale was defined based on the Celsius scale.



If we look at Fahrenheit, we have



C = (F - 32)*5/9

K = (F - 32)*5/9 + 273



K2 - K1 = [(F2 - 32)*5/9 + 273] - [(F1 - 32)*5/9 + 273]

K2 - K1 = (F2 - 32)*5/9 + 273 - (F1 - 32)*5/9 - 273

K2 - K1 = (F2 - 32)*5/9 - (F1 - 32)*5/9

K2 - K1 = [(F2 - 32) - (F1 - 32)]*5/9

K2 - K1 = [F2 - 32 - F1 + 32]*5/9

K2 - K1 = (F2 - F1)*5/9



Let's try that out with our case of a -20 K change in temperature, and see if we get the same answer.



-20 = (F2 - F1)*5/9

-20 * 9/5 = F2 - F1

F2 - F1 = -36 掳F



Yep, it works! I hope this helps you out!Temperature change in bottle?
You are correct in considering absolute zero but have you guessed at the initial temperature of the drink?