To solve the problem of calculating the amount of heat absorbed by a 12g piece of iron when its temperature increases from 20°C to 30°C, with a specific heat capacity of 0.46 J/g°C, follow these detailed steps:
1. Identify the given values:
- Mass of the iron piece, [tex]\( m = 12 \)[/tex] grams
- Initial temperature, [tex]\( T_{\text{initial}} = 20 \)[/tex]°C
- Final temperature, [tex]\( T_{\text{final}} = 30 \)[/tex]°C
- Specific heat capacity of iron, [tex]\( c = 0.46 \)[/tex] J/g°C
2. Calculate the change in temperature ([tex]\( \Delta T \)[/tex]):
[tex]\[
\Delta T = T_{\text{final}} - T_{\text{initial}}
\][/tex]
Substituting the given temperatures:
[tex]\[
\Delta T = 30 °C - 20 °C = 10 °C
\][/tex]
3. Use the formula for heat absorbed or released:
[tex]\[
q = m \cdot c \cdot \Delta T
\][/tex]
where
- [tex]\( q \)[/tex] is the amount of heat absorbed
- [tex]\( m \)[/tex] is the mass of the substance
- [tex]\( c \)[/tex] is the specific heat capacity
- [tex]\( \Delta T \)[/tex] is the change in temperature
4. Substitute the given values into the formula:
[tex]\[
q = 12 \text{ g} \cdot 0.46 \text{ J/g°C} \cdot 10 °C
\][/tex]
5. Perform the multiplication:
[tex]\[
q = 12 \cdot 0.46 \cdot 10
\][/tex]
[tex]\[
q = 55.2 \text{ J}
\][/tex]
Therefore, the amount of heat absorbed by the 12g piece of iron as it heats up from 20°C to 30°C is 55.2 Joules.
