PLEASE HELP: define a, in terms of B and T

dajbuzimie

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Apr 25, 2007
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alpha is defined as:

alpha = (1/Rt) (dRt/dT)

Rt = Resistance Final
alpha = sensitivity
Ro = initial resistance
Beta = constant
Tinitial = Temperature initial
T final = temperature final

I need to derive an expression for alpha in terms of (beta) and T

I am given that Rt = (Ro) * exp (beta*(1/T_final - 1/T_initial))
 
You haven't provided any relationship between beta, on the one hand, and the formula and its variables, on the other. Nor do R<sub>0</sub>, T<sub>i</sub>, and T<sub>f</sub> appear to come into play.

Without any way of relating the information, I see no way of "solving" for alpha in terms of these (apparently unrelated) variables. Sorry.

Eliz.
 
Hello, dajbuzimie!

There must be a typo . . .


\(\displaystyle \alpha\text{ is defined as: }\L\,\alpha \:=\:\frac{1}{R_t}\left(\frac{dR_t}{dT}\right)\;\) [1]

\(\displaystyle \text{and: }\L\,R_t \:=\: R_o\,\cdot\,e^{\beta(\frac{1}{T_F}\,-\,\frac{1}{T_I})}\;\) [2]

Derive an expression for \(\displaystyle \alpha\) in terms of \(\displaystyle \beta\) and \(\displaystyle T.\)

According to [2]: \(\displaystyle \L\:\frac{dR_t}{dT} \:=\:0\) . . . Therefore: \(\displaystyle \:\alpha \:=\:0\)

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

I could guess that [2] is missing a \(\displaystyle T\).

Those subscripts are annoying ... I'll simplify the equations.


\(\displaystyle \L\alpha\:=\:\frac{1}{R}\left(\frac{dR}{dt}\right)\;\) [1]

\(\displaystyle \L R \:=\:R_o\,\cdot\,e^{\beta(\frac{1}{p}-\frac{1}{q})T}\;\) [2]


Then: \(\displaystyle \L\:\frac{dR}{dT} \:=\:R_o\,\cdot\,e^{\beta(\frac{1}{p}-\frac{1}{q})T}\cdot\,\beta\left(\frac{1}{p}\,-\,\frac{1}{q}\right)\)


Hence: \(\displaystyle \L\:\alpha \:=\:\frac{1}{R_o\cdot e^{\beta(\frac{1}{p}-\frac{1}{q})T}}\,\cdot\,R_o\cdot e^{\beta(\frac{1}{p}-\frac{1}{q})T}\cdot\beta(\frac{1}{p}\,-\,\frac{1}{q})\)


Therefore: \(\displaystyle \L\:\alpha\:=\:\beta\left(\frac{1}{p}\,-\,\frac{1}{q}\right)\)

 
soroban said:
Hello, dajbuzimie!

There must be a typo . . .
Thanks for your help...but I think that I might have used the T final and T initial in the wrong way.

T final is actually just T. So there is a T in the equation.

The answer is
a = (-B^2/T2) exp (B/T-Ti)

I have no idea how they get this...
 
stapel said:
You haven't provided any relationship between beta, on the one hand, and the formula and its variables, on the other. Nor do R<sub>0</sub>, T<sub>i</sub>, and T<sub>f</sub> appear to come into play.

Without any way of relating the information, I see no way of "solving" for alpha in terms of these (apparently unrelated) variables. Sorry.
B is a constant in the equation
I think I might have described T in the wrong way...
Tf = T and
Ti = To

To and Ro are related because they are the same points
Ro at To
 
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