What Went Wrong with This Linear Temperature Scale Problem?

In summary, the problem involves finding the temperature of 146 K on a linear temperature scale where water boils at -40.0°X and freezes at -174°X. The solution involves using the slope formula and results in a final answer of -129.4°X.
  • #1
jdawg
367
2

Homework Statement



I'm not sure what I'm doing wrong on this problem! Please help :)

Suppose that on a linear temperature scale X, water boils at -40.0°X and freezes at -174°X. What is a temperature of 146 K on the X scale? (Approximate water's boiling point as 373 K.)

Homework Equations





The Attempt at a Solution



(K1,X1)=(373, -40)
(K2,X2)=(273, -174)

m=(X2-X1)/(K2-K1)=0.74627 X per K

X-X1=m(K-K1)
X=0.74627K-238.358
X=0.74627(146)-238.358
X= -129.4
 
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  • #2
For m, I get 1.34.

Chet
 
  • #3
I tried plugging in that slope into the formula and my online homework wouldn't accept the answer I got. Is the slope not X/K?
 
  • #4
Never mind, I messed up when I entered it into my calculator! Thanks so much!
 
  • #5
°X




It looks like you have correctly used the given data points to determine the slope of the linear temperature scale and then used the equation for a straight line to find the temperature of 146 K on the X scale. However, the resulting temperature of -129.4°X seems to be outside of the range given for water's boiling and freezing points on the X scale. It is possible that there was an error in the given data or in your calculations. I would recommend double checking your work and the given data to see if you can identify any mistakes. It may also be helpful to plot the data points and your line on a graph to visually check your solution. If you are still having trouble, I would suggest seeking assistance from a classmate, teacher, or tutor. Good luck!
 

Related to What Went Wrong with This Linear Temperature Scale Problem?

1. What is a linear temperature scale?

A linear temperature scale is a system for measuring temperature that uses a uniform interval between each degree, resulting in a linear relationship between the scale's units and the actual temperature. In other words, each unit on the scale represents an equal difference in temperature.

2. How is a linear temperature scale different from other temperature scales?

Unlike other temperature scales, such as the Celsius or Fahrenheit scales, a linear temperature scale has equal intervals between each degree. This means that the difference between 10 and 20 degrees on the scale is the same as the difference between 80 and 90 degrees, making it a more precise and consistent way to measure temperature.

3. What is the most commonly used linear temperature scale?

The most commonly used linear temperature scale is the Kelvin scale. It is often used in scientific and technical applications because it has a true zero point, meaning that 0 Kelvin represents absolute zero, the lowest possible temperature.

4. Can a linear temperature scale be used to measure negative temperatures?

Yes, a linear temperature scale can be used to measure negative temperatures. The Kelvin scale, for example, extends infinitely in both positive and negative directions, with 0 Kelvin representing absolute zero. This means that negative temperatures can be represented on a linear temperature scale, unlike other scales where negative temperatures are not possible.

5. How is a linear temperature scale calibrated?

A linear temperature scale is typically calibrated using two fixed points, such as the freezing and boiling points of water. These points are assigned specific values on the scale, and the intervals between them are divided into equal units, creating a linear relationship between the scale's units and the actual temperature.

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