If temperature scale is changed from `'^(@)C` to `'^(@)F`, the numerical value of specific heat

Options

A. increase
B. decrease
C. remains unchanged
D. none of these

Answer

To solve the problem of how the numerical value of specific heat changes when the temperature scale is changed from Celsius (°C) to Fahrenheit (°F), we can follow these steps:

### Step-by-Step Solution:

1. **Understand Specific Heat**: Specific heat (S) is defined as the amount of heat required to change the temperature of a unit mass of a substance by one degree. It is usually expressed in units like J/(kg·°C) or J/(kg·°F).

2. **Temperature Conversion Formula**: The relationship between Celsius and Fahrenheit is given by the formula:
\[ F = \frac{9}{5}C + 32 \]
This can also be rearranged to express the change in temperature:
\[ \Delta F = \frac{9}{5} \Delta C \]

3. **Change in Temperature**: When we change the temperature scale, we need to consider how a change in temperature in Celsius relates to a change in temperature in Fahrenheit. From the formula above, we can derive:
\[ \Delta C = \frac{5}{9} \Delta F \]

4. **Relating Specific Heat in Different Scales**: The specific heat in Celsius (S_C) and Fahrenheit (S_F) can be related using the change in temperature:
\[ S_C = \frac{Q}{m \Delta C} \]
\[ S_F = \frac{Q}{m \Delta F} \]

5. **Substituting the Change in Temperature**: Now, substituting \(\Delta C\) in terms of \(\Delta F\):
\[ S_F = \frac{Q}{m \Delta F} = \frac{Q}{m \left(\frac{5}{9} \Delta C\right)} = \frac{9}{5} \cdot \frac{Q}{m \Delta C} = \frac{9}{5} S_C \]

6. **Final Relation**: This shows that:
\[ S_C = \frac{5}{9} S_F \]
Therefore, if you convert specific heat from Celsius to Fahrenheit, the specific heat in Fahrenheit is:
\[ S_F = \frac{9}{5} S_C \]

### Conclusion:
When converting specific heat from Celsius to Fahrenheit, the numerical value of specific heat decreases by a factor of \(\frac{5}{9}\). Thus, the specific heat in Fahrenheit is \(\frac{5}{9}\) times that in Celsius.