Question

If, in defining the specific heat, the temperature is represented in \[{}^\circ F\] instead of \[{}^\circ C\] then the numerical value of specific heat will
A) be converted to heat capacity
B) remain unchanged
C) decrease
D) increase

Answer 1

Hint: Specific heat refers to the ratio of the quantity of heat that we require to raise the temperature of a body by one degree that we need to increase the temperature of an equivalent mass of liquid (water) by one degree. Heat capacity represents the ability of a substance to absorb heat energy.

Complete step by step solution:
Let’s say \[Q\] amount of heat is needed to raise the temperature of a body of certain mass by \[1{}^\circ C\] and amount of heat is needed to raise the temperature of an equivalent mass of water by \[1{}^\circ C\]
From the definition of specific heat mentioned in the hint, specific heat can be given as \[\dfrac{Q}{q}\]
Now we all know that \[180\] divisions on the Fahrenheit scale correspond to \[100\] divisions of the Celsius scale.
Hence we can say that \[1{}^\circ F\] corresponds to \[{{\left( \dfrac{100}{180} \right)}^{{}^\circ }}C={{\left( \dfrac{5}{9} \right)}^{{}^\circ }}C\]
Hence the amount of heat needed to raise the temperature of the substance by one degree on the Fahrenheit will be \[\left( \dfrac{5}{9} \right)Q\]
Similarly, the amount of heat needed to raise the temperature of water by one degree on the Fahrenheit scale will be \[\left( \dfrac{5}{9} \right)q\]
Calculating the new specific heat corresponding to degree Fahrenheit, we get
specific heat \[=\dfrac{\left( \dfrac{5}{9} \right)Q}{\left( \dfrac{5}{9} \right)q}=\dfrac{Q}{q}\]
Hence we can clearly see that the specific heat remains unchanged even if the temperature is represented on the Fahrenheit scale instead of the Celsius scale.

Hence, Option (B) is the correct answer.

Note:Students often get confused with specific heat and specific heat capacity and end up doing blunders. Specific heat is a ratio whereas specific heat capacity is a measure of the amount of heat necessary to raise the temperature of one gram of a pure substance by one degree. Be mindful of the difference.