To calculate the amount of heat required to raise the temperature of water, we can use the formula:
[tex]\[ q = m \cdot c \cdot \Delta T \][/tex]
Where:
- [tex]\( q \)[/tex] is the heat required (in joules, J),
- [tex]\( m \)[/tex] is the mass of the water (in grams, g),
- [tex]\( c \)[/tex] is the specific heat capacity of water (in J/g·°C),
- [tex]\( \Delta T \)[/tex] is the change in temperature (in °C).
Given:
- The mass of water, [tex]\( m = 23.1 \)[/tex] g,
- The initial temperature, [tex]\( T_{initial} = 1.8 \)[/tex] °C,
- The final temperature, [tex]\( T_{final} = 33.2 \)[/tex] °C,
- The specific heat capacity of water, [tex]\( c = 4.186 \)[/tex] J/g·°C.
First, we calculate the temperature change [tex]\( \Delta T \)[/tex]:
[tex]\[ \Delta T = T_{final} - T_{initial} \][/tex]
[tex]\[ \Delta T = 33.2 \, °C - 1.8 \, °C \][/tex]
[tex]\[ \Delta T = 31.4 \, °C \][/tex]
Next, we use the formula to find the heat required:
[tex]\[ q = m \cdot c \cdot \Delta T \][/tex]
[tex]\[ q = 23.1 \, \text{g} \cdot 4.186 \, \frac{\text{J}}{\text{g·°C}} \cdot 31.4 \, °C \][/tex]
[tex]\[ q = 23.1 \cdot 4.186 \cdot 31.4 \][/tex]
[tex]\[ q = 3042.86844 \, \text{J} \][/tex]
Finally, we round the result to two decimal places:
[tex]\[ q \approx 3042.87 \, \text{J} \][/tex]
So, the heat required to raise the temperature of 23.1 g of water from 1.8°C to 33.2°C is approximately 3042.87 J.
