To calculate the amount of heat required to raise the temperature of 500 grams of water from [tex]\(15^{\circ} C\)[/tex] to [tex]\(85^{\circ} C\)[/tex], we will use the specific heat formula:
[tex]\[ Q = mc\Delta T \][/tex]
where:
- [tex]\( Q \)[/tex] is the heat energy in joules (J)
- [tex]\( m \)[/tex] is the mass of the substance in grams (g)
- [tex]\( c \)[/tex] is the specific heat capacity in joules per gram per degree Celsius (J/g°C)
- [tex]\( \Delta T \)[/tex] is the change in temperature in degrees Celsius (°C)
Let's break down the steps below:
1. Identify the given values:
- Mass of water, [tex]\( m \)[/tex] = 500 grams.
- Initial temperature, [tex]\( T_{\text{initial}} \)[/tex] = [tex]\( 15^{\circ} C \)[/tex].
- Final temperature, [tex]\( T_{\text{final}} \)[/tex] = [tex]\( 85^{\circ} C \)[/tex].
- Specific heat capacity of water, [tex]\( c \)[/tex] = 4.18 J/g°C.
2. Calculate the temperature change [tex]\(\Delta T\)[/tex]:
[tex]\[
\Delta T = T_{\text{final}} - T_{\text{initial}} = 85^{\circ} C - 15^{\circ} C = 70^{\circ} C
\][/tex]
3. Plug the values into the specific heat formula to find the heat energy (Q):
[tex]\[
Q = m \cdot c \cdot \Delta T
\][/tex]
Substituting the values:
[tex]\[
Q = 500 \, \text{g} \cdot 4.18 \, \text{J/g°C} \cdot 70^{\circ} C
\][/tex]
4. Calculate the heat energy (Q) in joules:
[tex]\[
Q = 500 \cdot 4.18 \cdot 70
\][/tex]
[tex]\[
Q = 146300 \, \text{J}
\][/tex]
5. Convert joules to kilojoules (1 kJ = 1000 J):
[tex]\[
\text{Heat required in kilojoules} = \frac{Q}{1000} = \frac{146300 \, \text{J}}{1000} = 146.3 \, \text{kJ}
\][/tex]
Therefore, the amount of heat required to raise the temperature of 500 grams of water from [tex]\(15^{\circ} C\)[/tex] to [tex]\(85^{\circ} C\)[/tex] is [tex]\(146.3\)[/tex] kJ.
