Find the change in the temperature on the Fahrenheit scale and on Kelvin scale, if an iron piece is heated from `30^(@)C" to "90^(@)C`.

Options

A. `108^(@)F, 60K`
B. `100^(@)F, 55K`
C. `100^(@)F, 65K`
D. `60^(@)F, 108K`

Answer

To find the change in temperature on the Fahrenheit scale and the Kelvin scale when an iron piece is heated from \(30^\circ C\) to \(90^\circ C\), we will follow these steps:

### Step 1: Calculate the change in temperature in Celsius
The change in temperature in Celsius (\(\Delta C\)) can be calculated using the formula:
\[ \Delta C = T_{\text{final}} - T_{\text{initial}} = 90^\circ C - 30^\circ C = 60^\circ C \]

### Step 2: Convert the change in Celsius to Kelvin
The change in temperature in Kelvin (\(\Delta K\)) is the same as the change in Celsius since the size of the degree is the same:
\[ \Delta K = \Delta C = 60 \text{ K} \]

### Step 3: Convert the change in Celsius to Fahrenheit
To convert the change in temperature from Celsius to Fahrenheit, we use the formula:
\[ \Delta F = \frac{9}{5} \Delta C \]
Substituting the value of \(\Delta C\):
\[ \Delta F = \frac{9}{5} \times 60 = 108^\circ F \]

### Summary of Results
- Change in temperature on the Kelvin scale: \(60 \text{ K}\)
- Change in temperature on the Fahrenheit scale: \(108^\circ F\)

### Final Answer
The change in temperature is:
- **Fahrenheit:** \(108^\circ F\)
- **Kelvin:** \(60 \text{ K}\)

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