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Temperature Scales

3 questions

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Question 1Question →

A mechanic checks a heavy-duty engine's coolant temperature gauge, which displays a reading of 35∘C35^\circ\text{C}. What is this temperature reading in degrees Fahrenheit?

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Answer: 95

Answer

95
The correct answer is derived by multiplying the given Celsius value by 9/5 to adjust for the difference in degree size, and then adding 32 to account for the difference in the freezing point baselines of the two scales.

Step-by-Step Solution

1
Identify the proper conversion formula.
F=95C+32F = \frac{9}{5}C + 32
This is the mathematical relationship used to convert temperatures from the Celsius scale to the Fahrenheit scale.
2
Substitute the given Celsius value into the formula.
F=95(35)+32F = \frac{9}{5}(35) + 32
The gauge reading is exactly 35∘C35^\circ\text{C}.
3
Calculate the proportional factor.
63+3263 + 32
Dividing 35 by 5 yields 7, and multiplying 7 by 9 yields 63.
4
Add the baseline offset to find the final temperature.
95
The Fahrenheit scale offset is 32 degrees above the freezing point equivalent.

Key Concept

Celsius to Fahrenheit Conversion
Question 2Question →

An industrial oven used for curing aerospace composites is set to a precise temperature of 680∘F680^\circ\text{F}. To program a secondary backup sensor that operates exclusively on the Celsius scale, what numerical value must the technician enter?

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Answer: 360

Answer

360
The correct equivalent temperature is found by first subtracting 32 from the Fahrenheit value to adjust for the different zero points, resulting in 648648. Multiplying this difference by 59\frac{5}{9} accounts for the different degree increments between the scales, producing an exact value of 360∘C360^\circ\text{C}.

Step-by-Step Solution

1
Set up the conversion equation.
C=59(680−32)C = \frac{5}{9}(680 - 32)
This is the standard formula to convert degrees Fahrenheit into degrees Celsius.
2
Perform the subtraction inside the parentheses.
680−32=648680 - 32 = 648
According to the order of operations, the offset between the two temperature scales must be removed first.
3
Multiply the difference by the fraction 59\frac{5}{9}.
648÷9=72648 \div 9 = 72, then 72×5=36072 \times 5 = 360
Multiplying by 59\frac{5}{9} scales the Fahrenheit degree magnitude to match the Celsius degree magnitude.

Key Concept

Temperature Scale Conversion
Question 3Question →

During a performance test of an aviation hydraulic system, the operating fluid experiences a temperature increase of 45∘C45^{\circ}\text{C}. What is the equivalent temperature increase measured in degrees Fahrenheit?

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Answer: 81∘F81^{\circ}\text{F}

Answer

The correct equivalent temperature increase is 81∘F81^{\circ}\text{F}.
A change of 1∘C1^{\circ}\text{C} corresponds exactly to a change of 1.8∘F1.8^{\circ}\text{F} (which is the fraction 95\frac{9}{5}). Because we are evaluating a change in temperature (an interval) rather than converting an absolute point on the thermometer, we only multiply by the ratio and do not add the 32∘32^{\circ} offset. Multiplying the 45∘C45^{\circ}\text{C} increase by 95\frac{9}{5} results in an 81∘F81^{\circ}\text{F} increase.

Step-by-Step Solution

1
Recognize that the question asks for a temperature interval (an increase), not a specific absolute temperature.
The +32+32 offset used in standard conversions is excluded.
The offset only aligns the starting points of the scales (0∘C0^{\circ}\text{C} vs 32∘F32^{\circ}\text{F}). When measuring a change (ΔT\Delta T), only the ratio of the degree sizes matters.
2
Apply the ratio of Fahrenheit degrees to Celsius degrees (95\frac{9}{5}) to the given temperature increase.
ΔF=45×95\Delta F = 45 \times \frac{9}{5}
One degree Celsius is equal in magnitude to 1.81.8 (or 95\frac{9}{5}) degrees Fahrenheit.
3
Calculate the final value.
45÷5=945 \div 5 = 9; 9×9=81∘F9 \times 9 = 81^{\circ}\text{F}.
Completing the arithmetic gives the equivalent magnitude of the temperature change.

Key Concept

Temperature Scale Intervals (ΔT\Delta T)

Alternative Method

You can pick any starting temperature to prove the interval. If the fluid starts at 0∘C0^{\circ}\text{C} (32∘F32^{\circ}\text{F}) and goes to 45∘C45^{\circ}\text{C} (113∘F113^{\circ}\text{F}), the difference is 113∘F−32∘F=81∘F113^{\circ}\text{F} - 32^{\circ}\text{F} = 81^{\circ}\text{F}.
Estimated Time:45s
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