JAMB 2019 Physics · Question 83

A thermocouple thermometer is connected to a millivoltmeter which can read up to 10mV. When one junction is in…

Question

A thermocouple thermometer is connected to a millivoltmeter which can read up to 10mV. When one junction is in ice at 0°C and the other is steam at 100°C, the millivoltmeter reads 4mV. What is the maximum temperature which this arrangement can measure

A.100 $^o$ C
B.248 $^o$ C
C.250 $^o$ C
D.350 $^o$ C

Answer: C. 250 $^o$ C

Explanation written with AI and checked against the answer key

Analysis

To solve this problem, we need to understand the relationship between the electromotive force (e.m.f.) produced by a thermocouple and the temperature difference between its junctions. For most thermocouples within a reasonable range, the e.m.f. ( $E$ ) is directly proportional to the temperature difference ( $\Delta\theta$ ) between the cold junction and the hot junction.

Concept

The formula for this linear relationship is:

E = k \times (\theta_h - \theta_c)

Where:

$E$ = e.m.f. in millivolts (mV)
$k$ = a constant for the thermocouple
$\theta_h$ = temperature of the hot junction
$\theta_c$ = temperature of the cold junction (in this case, 0°C)

Step-by-Step Solution

Step 1: Find the constant ( $k$ ) using the given data. We are told that when the hot junction is at 100°C and the cold junction is at 0°C, the reading is 4mV.

4\text{mV} = k \times (100^\circ\text{C} - 0^\circ\text{C})

4 = k \times 100

k = \frac{4}{100} = 0.04 \text{ mV/}^\circ\text{C}

Step 2: Calculate the maximum temperature. The millivoltmeter has a maximum reading of 10mV. We want to find the temperature ( $\theta_{max}$ ) that corresponds to this 10mV reading, keeping the cold junction at 0°C.

E_{max} = k \times (\theta_{max} - 0^\circ\text{C})

10 = 0.04 \times \theta_{max}

Step 3: Solve for $\theta_{max}$ .

\theta_{max} = \frac{10}{0.04}

\theta_{max} = \frac{1000}{4}

\theta_{max} = 250^\circ\text{C}

Conclusion

The arrangement can measure up to a maximum temperature of 250°C. This matches option C.

Exam Tip

When dealing with thermocouple problems in JAMB, always check if the cold junction is at 0°C (ice point). If the cold junction were at a different temperature (e.g., room temperature), you would have to account for that in your $\Delta\theta$ calculation. Also, remember that the relationship is linear only within a specific range; for higher temperatures, the relationship becomes non-linear, but for JAMB physics, you can safely assume linearity unless stated otherwise.

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