Twice as Cold as ZeroDate: 04/28/99 at 15:03:30 From: Daniel Carlson Subject: 0 degrees x2 I've asked and wondered about this a lot but have found no good answer so far. What is the temperature if it's twice as cold [or warm] as zero degrees? Date: 04/29/99 at 12:35:35 From: Doctor Nbrooke Subject: Re: 0 degrees x2 Hello, and thanks for writing to Dr. Math. You pose a very interesting question. What is the temperature if it's twice as cold as zero degrees? The Fahrenheit and Celsius temperature scales are "relative" temperature scales, in that they are both relative to a couple of specific temperatures, namely the freezing and boiling points of water. Let's make your question a little more specific: "What is the temperature if it's twice as warm as 0 degrees Celsius (the freezing point of water)?" To answer this question we need to convert this Celsius temperature to an "absolute" temperature scale, a scale with no negative temperatures. We'll use the Kelvin scale. 0 degrees Kelvin is the point at which all motion in matter stops; it is known as "absolute zero." No temperature can exist that is lower than 0 degrees Kelvin. The formula to convert from Celsius to Kelvin temperature is K = C + 273.15, where K is the Kelvin temperature and C is the Celsius temperature. So 0 degrees Celsius is equal to 273.15 degrees Kelvin. We can double this number to get 546.30, the temperature that is twice as warm as 0 degrees Celsius. We can then subtract 273.15 from our answer to convert it back to the Celsius scale. The temperature is 273.15 degrees Celsius when it is twice as warm as 0 degrees Celsius. Makes perfect sense, doesn't it? Thanks for writing, and write back any time. - Doctor Nbrooke, The Math Forum http://mathforum.org/dr.math/ Date: 11/09/1999 at 19:26:41 From: Lynn X. Subject: Double of zero degrees? I received an email with an interesting question and I would like to know the answer. If someone tells you that it is zero degrees outside, and tomorrow it will be twice as cold, what will the temperature be tomorrow? Date: 11/10/1999 at 11:37:55 From: Doctor Rick Subject: Re: Double of zero degrees? Hi, Lynn. There is no really good answer to this question; the term "twice as cold" is not well defined. A physicist might want to define it one way, but someone deciding what to wear would have good reason for defining it in a very different way. To the best of my knowledge, no one has actually defined it quantitatively, in either of these ways or any other way. Still, I will tell you my ideas on two ways "twice as cold" *could* be defined if you insisted on doing so. "Cold" is confusing in the same way that "short" or "small" is confusing. If I say that I am twice as short as you, what I probably mean is that I am half as tall as you. It isn't really a good way to talk at all; it's best to say "half as tall" because it's less confusing. "Cold" is even more confusing than "short" because temperatures can be negative, but height can never be negative (not the height of a person, anyway). If "twice as cold" means "half the temperature", then if the temperature is negative, "twice as cold" is *warmer*! For instance, half of -10 degrees is -5 degrees, which is warmer than -10 degrees. If "twice as cold" meant "twice the temperature", it would go in the right direction for negative temperatures, but not for positive temperatures. Then, too, there's the problem that "twice as cold" will mean different things depending on whether you are using the Celsius or Fahrenheit scale. "Twice as cold" as 0 C is 0 C, but 0 C is 32 F, and half of this is 16 F, which is -8.9 C. One solution is to choose a meaningful zero point for temperature. Physicists determined that temperature has to do with how much energy there is in the air (or whatever you're taking the temperature of.) This energy is all gone when you get down to a temperature of -273.15 degrees Celsius, or about -460 degrees Fahrenheit. This temperature is called "absolute zero." The scientists then invented two new temperature scales: Kelvin, which is the degrees C plus 273.15, and Rankine, which is the degrees F plus 460. That means that 0 degrees on either scale is absolute zero. Therefore I propose that if you insist on saying "twice as cold," we should mean this by it: "half the temperature on the Kelvin (or Rankine) scale." By this definition, "twice as cold as 0 C" is half of 273.15 K, which is 136.57 K. Converting this back to Celsius, we get -136.58 C. That's very cold. I don't think it will ever be "twice as cold as 0 degrees" in either Fahrenheit or Celsius. This definition of "twice as cold" might satisfy a low-temperature physicist, who is concerned about the amount of energy in a substance, but it does not agree with our everyday idea of cold. Our everyday use of "twice as cold" might be something like, "It's so cold that I need to wear twice as much clothing." If I wanted to invent a mathematical meaning for "twice as cold" that would fit this idea, I would pick a temperature that is neither warm nor cold, perhaps 65 F. Then "how cold it is" would mean "how many degrees below 65 F," and "how hot it is" would mean "how many degrees above 65." Then 45 F would be "twice as cold" as 55 F, and -65 F would be twice as cold as 0 F. (That's still very cold!) You can see that this is a very different definition from the first one. It makes more sense according to our everyday idea of cold, but it has one problem: some international agency has to set that "neither cold nor warm" temperature. Judging from the battles some families have over thermostat settings, I don't think this will be easy! So I say again, I would rather avoid the phrase "twice as cold" altogether. - Doctor Rick, The Math Forum http://mathforum.org/dr.math/ |
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