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Chapter 21: Problem 8

A thermocouple is formed from two different metals, joined at two points in such a way that a small voltage is produced when the two junctions are at different temperatures. In a particular iron-constantan thermocouple, with one junction held at \(0^{\circ} \mathrm{C}\), the output voltage varies linearly from 0 to \(28.0 \mathrm{mV}\) as the temperature of the other junction is raised from 0 to \(510^{\circ} \mathrm{C}\). Find the temperature of the variable junction when the thermocouple output is \(10.2 \mathrm{mV}\).

Short Answer

Expert verified
The temperature of the variable junction when the thermocouple output is \(10.2 \, \mathrm{mV}\) is approximately \(186^{\circ} \mathrm{C}\)

Step by step solution

01

Identify the Variation

Understand that the relationship between temperature and voltage is linear, which means it can be written in the form y = mx + c. Here, 'y' represents the voltage, 'x' is the temperature, 'm' is the slope, and 'c' is the y-intercept.
02

Calculate the Slope

Calculate the slope of the linear equation by using the formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\), which results in \(m = \frac{28 - 0}{510 - 0} = 0.0549 \, \mathrm{mV/°C}\). Record this value as it will be used to calculate the temperature.
03

Apply the Thermocouple Output

When the thermocouple output is \(10.2 \, \mathrm{mV}\), substitute 'y' in the equation with '10.2' and the value of 'm' as '0.0549' to solve for 'x' (the temperature in °C). This results in \(10.2 = 0.0549x + c\), since the output voltage is '0' at '0°C', it means that 'c' is '0'.
04

Solve the Equation

Solve for 'x' (the temperature of the variable junction) using the rearranged equation from step 3, \(x = \frac{10.2}{0.0549}\).

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Most popular questions from this chapter

The best vacuum that can be attained in the laboratory corresponds to a pressure of about \(10^{-18} \mathrm{~atm}\), or \(1.01 \times 10^{-13} \mathrm{~Pa}\). How many molecules are there per cubic centimeter in such a vacuum at \(22^{\circ} \mathrm{C} ?\)

A resistance thermometer is a thermometer in which the electrical resistance changes with temperature. We are free to define temperatures measured by such a thermometer in kelvins (K) to be directly proportional to the resistance \(R\), measured in ohms \((\Omega) .\) A certain resistance thermometer is found to have a resistance \(R\) of \(90.35 \Omega\) when its bulb is placed in water at the triple-point temperature \((273.16 \mathrm{~K}) .\) What temperature is indicated by the thermometer if the bulb is placed in an environment such that its resistance is \(96.28 \Omega ?\)

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