# Temperature Variance with Resistivity

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1. Mar 25, 2015

### minimario

1. The problem statement, all variables and given/known datati
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?

2. Relevant equations

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

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: Mar 25, 2015
2. Mar 25, 2015

### ehild

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. Mar 25, 2015

### minimario

Yes, that is what I did in the first calculation; however, the book performs the second calculation (and obtains diff. answer)

4. Mar 25, 2015

### ehild

from where is 185 from?????

5. Mar 25, 2015

### minimario

I changed it to 215, which is 235 - 20.

6. Mar 26, 2015

### minimario

Anyone can figure out problem?

7. Mar 26, 2015

### ehild

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. Mar 26, 2015

### minimario

...are you sure? I'm fairly confident it's a decent book :/

9. Mar 26, 2015