To calculate the heat gained by the water, we can use the formula:
\[ Q = mc\Delta T \]
Where:
- \( Q \) is the heat gained (in kJ),
- \( m \) is the mass (in kg),
- \( c \) is the specific heat capacity (in kJ/kg°C),
- \( \Delta T \) is the change in temperature (in °C).
Given:
- \( m = 4.0 , \text{kg} \)
- \( c = 4.186 , \text{kJ/kg°C} \)
- Initial temperature \( T_i = 10°C \) and final temperature \( T_f = 15°C \)
First, calculate the change in temperature:
\[ \Delta T = T_f - T_i = 15°C - 10°C = 5°C \]
Now we can plug these values into the formula:
\[ Q = (4.0 , \text{kg}) \times (4.186 , \text{kJ/kg°C}) \times (5°C) \]
\[ Q = 4.0 \times 4.186 \times 5 = 83.72 , \text{kJ} \]
Rounding this value, we find:
\[ Q \approx 84 , \text{kJ} \]
So, the heat gained by the water is 84 kJ.
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