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Zorluk: OrtaTemperature Scales

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?

  1. A
    25∘F25^{\circ}\text{F}
  2. B
    57∘F57^{\circ}\text{F}
  3. 81∘F81^{\circ}\text{F}Cevap
  4. D
    113∘F113^{\circ}\text{F}

Cevap

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.

Adım Adım Çözüm

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.

Anahtar Kavram

Temperature Scale Intervals (ΔT\Delta T)

Alternatif Yöntem

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}.
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Temperature Scales

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