Question

If temperature scale is changed from C to F, numerical value of specific heat will:
A. Increase
B. Decrease
C. Remain the same
D. Can’t decide

Answer 1

Specific heat can be defined as the heat required to raise the temperature of 1 gram mass of substance by one degree. It is a unique property of a substance which is used for thermodynamic calculations.

Formula used: $F=\dfrac95 C+32$, where F is the temperature in Fahrenheit scale and C is the temperature in Celsius scale.

Complete step by step answer:
As specific heat is the amount of heat required to raise the temperature of unit mass by$1^{\circ}C$, Hence its clear if the other scale’s unit increment is not equal to the increment in Celsius scale, then specific heat in both scales must differ in value.
Now, as we want the relation in Celsius and Fahrenheit for change in scales, hence differentiating the equation:$F=\dfrac95 C+32$, we get
$\Delta F = \dfrac 95 \Delta C + 0=\dfrac 95 \Delta C$ [as differentiation of constant is zero]
Now, I temperature change is $1^{\circ}C$there for the temperature change in Fahrenheit scale is:
$\Delta F = \dfrac95 \times 1=\left(\dfrac 95\right) {\circ}F$
Hence, in other words we can say that specific heat is the heat required to raise the temperature of unit mass of a substance by $\left(\dfrac 95\right) {\circ}F$ .
But we are supposed to calculate it for $1^{\circ}F$. Hence to equalize both terms, we must divide the original specific heat by $\dfrac 95$. Hence the value specific heat in Fahrenheit will decrease by the factor of $\dfrac95$. Hence option B is correct.

Note:
One more way to answer this question could be that as $1^{\circ}C$(standard case) change is greater than $1^{\circ}F$(asked case) change, hence originally we need to provide more heat, to raise temperature by $1^{\circ}C$ and finally less heat must be provided. Hence finally specific heat, which is nothing but the amount of heat, will also decrease.