Question #119189

The resistance R of a platinum wire at temperature t°C, measured on the gas

scale is given by

R. R. (1 + aT +bT)

Where a = 3.8 x 10-³°C!

b = -5.6 x 10^7C.

What temperature will the platinum thermometer indicate when the

temperature on the gas scale is 200°C?

scale is given by

R. R. (1 + aT +bT)

Where a = 3.8 x 10-³°C!

b = -5.6 x 10^7C.

What temperature will the platinum thermometer indicate when the

temperature on the gas scale is 200°C?

Expert's answer

"R=R_0(1+aT+bT^2);"

"a=3.8\\sdot 10^{-3}(1\/^oC);"

"b=-5.6\\sdot10^{-7}(1\/^oC^2);"

"\\dfrac{R}{R_0}=1+3.8\\sdot10^{-3}(1\/^oC)\\sdot 200^oC-5.6\\sdot10^{-7}(1\/^oC^2)\\sdot(200^oC)^2="

"=1.7376;"

The temperature dependence of the resistance for most metals is close to linear for a wide range of temperatures and is described by the formula:

"R=R_0(1+\\alpha\\Delta T)" , "\\alpha-" is the temperature coefficient of electrical resistance

"\\alpha=0.003927(1\/^oC);"

"1+\\alpha\\Delta T=\\dfrac{R}{R_0}\\implies \\Delta T=\\dfrac{\\dfrac{R}{R_0}-1}{\\alpha};"

"\\Delta T=\\dfrac{1.7376-1}{0.003927}=187.8^oC;"

**Answer: **"\\Delta T=187.8^oC."

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