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 on the Kelvin scale when an iron piece is heated from \(30^\circ C\) to \(90^\circ C\), we can follow these steps:

### Step 1: Calculate the change in temperature in Celsius
The change in temperature (\(\Delta T\)) in Celsius is given by:
\[ \Delta T = T_{\text{final}} - T_{\text{initial}} = 90^\circ C - 30^\circ C = 60^\circ C \]

### Step 2: Convert the initial and final temperatures to Kelvin
To convert Celsius to Kelvin, we use the formula:
\[ T(K) = T(C) + 273 \]
- For \(30^\circ C\):
\[ T_{\text{initial}} = 30 + 273 = 303 \, K \]
- For \(90^\circ C\):
\[ T_{\text{final}} = 90 + 273 = 363 \, K \]

### Step 3: Calculate the change in temperature in Kelvin
The change in temperature in Kelvin is:
\[ \Delta T(K) = T_{\text{final}}(K) - T_{\text{initial}}(K) = 363 \, K - 303 \, K = 60 \, K \]

### Step 4: Convert the initial and final temperatures to Fahrenheit
To convert Celsius to Fahrenheit, we use the formula:
\[ T(F) = \left(\frac{9}{5} \times T(C)\right) + 32 \]
- For \(30^\circ C\):
\[ T_{\text{initial}} = \left(\frac{9}{5} \times 30\right) + 32 = 54^\circ F \]
- For \(90^\circ C\):
\[ T_{\text{final}} = \left(\frac{9}{5} \times 90\right) + 32 = 194^\circ F \]

### Step 5: Calculate the change in temperature in Fahrenheit
The change in temperature in Fahrenheit is:
\[ \Delta T(F) = T_{\text{final}}(F) - T_{\text{initial}}(F) = 194^\circ F - 54^\circ F = 140^\circ F \]

### Final Answers
- Change in temperature on the Kelvin scale: \(60 \, K\)
- Change in temperature on the Fahrenheit scale: \(140 \, F\)