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Temperature Variance with Resistivity

  • #1
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Homework Statement

ti[/B]
A resistance thermometer, which measures temperature by measuring the change in resistance of a conductor, is made of platinum and has a resistance of 50.0 Ohms? at 20.0°C. (a) When the device is immersed in a vessel containing melting indium, its resistance increases to 76.8 Ohms?. From this information, find the melting point of indium.

(b) The indium is heated further until it reaches a temperature of 235°C. What is the ratio of the new current in the platinum to the current Imp at the melting point?

Homework Equations



## R = R_0 [1+\alpha(T-T_0)] ##
##\alpha_{plat} = 3.92 \cdot 10^{-3}##

The Attempt at a Solution


For part (a), the answer is 157 degrees Celsius. (Says in the book as well)

Now, I'm getting 2 different answers for part (b) when using ## T_0 = 20## and ##T_0 = 157##.

When ##T_0 = 20##, the final resistance is ##50[1+\alpha \cdot 215] = 92.14##

When ##T_0 = 157##, the final resistance is ##76.8[1+\alpha \cdot 78] = 100.2##

Why the large discrepancy with calculating the same thing? (The 2nd one is correct, per the book)
 
Last edited:

Answers and Replies

  • #2
ehild
Homework Helper
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The resistance of the Pt thermometer is almost linear function of the temperature in a wide range.
You have to keep To= 20 C° and Ro=50 Ω, and calculate the resistance from the formula R(T) = Ro(1+α(T-To)).
 
  • #3
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Yes, that is what I did in the first calculation; however, the book performs the second calculation (and obtains diff. answer)
 
  • #4
ehild
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When ##T_0 = 20##, the final resistance is ##50[1+\alpha \cdot 185] = 86.26##
from where is 185 from?????
 
  • #5
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I changed it to 215, which is 235 - 20.
 
  • #6
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Anyone can figure out problem?
 
  • #7
ehild
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Anyone can figure out problem?
Read my post #2. The coefficient α=3.92⋅10−3 °C is valid if To=20 °C, Ro=50Ω. You can not use it for other To-s. The book is wrong.
Think: If the book was right, changing the temperature by a small amount dT and getting the resistance at T+dT, you would have the equation: R(T+dT)= R(T)(1+αdT).
If dt is small, R(T+dT) = R(T) +(dR/dT )dT, and the equation is equivalent to the differential equation dR/dT=αR(T), with the solution R(T)= RoeαT, an exponential function instead of a linear one.
 
  • #8
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...are you sure? I'm fairly confident it's a decent book :/
 
  • #9
ehild
Homework Helper
15,409
1,813

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