The temperature of an iron piece is heated from `30^@ C "to" 90^@ C`. What is the change in its temperature on the fahrenheit scale and on the kelvin scale?

Explanation

To solve the problem of finding the change in temperature of an iron piece heated from \(30^\circ C\) to \(90^\circ C\) on both the Fahrenheit and Kelvin scales, we can follow these steps:

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

### Step 2: Convert the Change in Temperature to Fahrenheit
To convert the change in temperature from Celsius to Fahrenheit, we use the formula:
\[ \Delta T_F = \Delta T_C \times \frac{9}{5} \]
Substituting the value of \(\Delta T_C\):
\[ \Delta T_F = 60^\circ C \times \frac{9}{5} = 60 \times 1.8 = 108^\circ F \]

### Step 3: Convert the Change in Temperature to Kelvin
The change in temperature in Kelvin (\(\Delta T_K\)) is the same as the change in temperature in Celsius because the size of the degree is the same. Therefore:
\[ \Delta T_K = \Delta T_C = 60 \, K \]

### Final Answers
- The change in temperature on the Fahrenheit scale is \(108^\circ F\).
- The change in temperature on the Kelvin scale is \(60 \, K\).