If the temperature of a body is increased by 5°C, then on Fahrenheit scale its temperature will increase by:

  1. 9°F
  2. 5°F
  3. 1.8°F
  4. None of these

Answer (Detailed Solution Below)

Option 1 : 9°F
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Detailed Solution

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CONCEPT:

Celsius scale:

  • In this scale, a lower fixed point (ice point) is taken 0° and the upper fixed point (steam point) is taken 100°.
  • On the Celsius scale, there are 100 equal intervals between two reference points.

Fahrenheit scale:

  • This scale of temperature has a lower fixed point at 32° F and an upper fixed point at 212° F.
  • On the Fahrenheit scale, there are 180 equal intervals between two reference points.

The relation between the Fahrenheit temperature (tF) and the Celsius temperature (tC) is given as,

\(⇒ \frac{t_F-32}{180}=\frac{t_C}{100}\)

\(⇒ t_F=\frac 95 t_C+32\)

CALCULATION:

Given ΔtC = 5°C

We know that the relation between the Fahrenheit temperature (tF) and the Celsius temperature (tC) is given as,

\(⇒ \frac{t_F-32}{180}=\frac{t_C}{100}\)

Let the temperature at first is C1 degree Celsius, and then it increased by 5° to C2 degree Celsius, hence the difference between the initial and final temperature is given by

C1 - C2 = 5

Let the temperature is F1 degree Fahrenheit corresponding to C1 degree Celsius and F2 degree Fahrenheit

When the temperature in degrees Celsius changed to C2 which can be calculated from the formula.

\({T_{\left( {^\circ F} \right)}}{\rm{ }} = \frac{9}{5} \times {\rm{ }}{T_{\left( {^\circ C} \right)\;}} + 32 \)

\(F_1 = C_ 1 \times \frac{9}{5}+32 \)

\(F_2 = C_ 2 \times \frac{9}{5}+32 \)

Then the difference in temperature in degrees Fahrenheit equal to

\(F_1 - F_2 = (C_1 - C_2) \times \frac{9}{5}\)

Where C1 - C2 = 5

\(F_1 - F_2 = 5 \times \frac{9}{5}= 9 ^\circ F\)

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