Question

The temperature of the first object is \[{36^ \circ }{\text{C}}\] and that of the second object${36^ \circ }{\text{F}}$. Which is hotter than the other?
$(A)$ First object
$(B)$ Second object
$(C)$ Both have the same hotness
$(D)$ Cannot be determined

Answer 1

Hint : To determine which body is hotter than the other, both the temperatures mentioned should have the same units. In this question, we can convert both the given temperatures to either degrees Celsius or degrees Fahrenheit using appropriate equations. Once both the temperatures of the bodies are converted into the same unit, the hotter body can be determined by analyzing which of the bodies has a higher value in temperature.

Formula used:
$^{\text{o}}{\text{F}} = \dfrac{9}{5}{{\text{ }}^{\text{o}}}{\text{C}} + 32$

Complete step-by-step solution:
The given information:
The temperature of the first body: \[{36^ \circ }{\text{C}}\]
The temperature of the second body: ${36^ \circ }{\text{F}}$
The question is to determine which body is hotter than the other.
To do that one must convert both the quantities to the same unit using the equation $^{\text{o}}{\text{F}} = \dfrac{9}{5}{{\text{ }}^{\text{o}}}{\text{C}} + 32$
Converting the temperature of the first body to Fahrenheit:
 $^{\text{o}}{\text{F}} = \dfrac{9}{5}{{\text{ }}^{\text{o}}}{\text{C}} + 32$
Substituting the value of the first body in degree Celsius in the above equation we get, ${ \Rightarrow ^{\text{o}}}{\text{F}} = (\dfrac{9}{5} \times 36) + 32$
Simplifying the equation we get,
${ \Rightarrow ^{\text{o}}}{\text{F}} = 64.8 + 32 = 96.8$
Hence by using this equation we have obtained the temperature of both the bodies in the same unit.
The temperature of the first body: ${96.8^ \circ }{\text{F}}$
The temperature of the second body: ${36^ \circ }{\text{F}}$
From this, we observe that the first body has a higher value in degree Fahrenheit than the second body. The first body is hotter than the second body by ${60.8^ \circ }{\text{F}}$
$(A)$The first body is hotter than the second body.
$(B)$The second object is not the hotter body. From the calculations, we have obtained that the first body is hotter than the second body.
$(C)$Both the bodies do not have the same hotness. The first body is hotter than the second body.
$(D)$This is not the correct option as we have determined the first body to be comparatively hotter than the second body.
Hence the right answer is in option $(A)$

Note: This question can also be solved by converting the temperature of both bodies to degrees Celsius. This conversion can be done using the equation$^{\text{o}}{\text{C}} = \dfrac{5}{9}{{\text{ }}^{\text{o}}}{\text{F - }}32$. Either way, by converting to degree Fahrenheit or degree Celsius we obtain the same answer. That is in this question the first body is hotter than the second body. In numerical type questions, care must be taken to convert all the temperatures mentioned to the same unit.