To calculate the amount of heat needed to raise the temperature of a substance, we can use the formula:
\[ q = m \cdot c \cdot \Delta T \]
where:
- \( q \) = heat absorbed or released (in joules)
- \( m \) = mass of the substance (in grams)
- \( c \) = specific heat capacity (in J/g-K)
- \( \Delta T \) = change in temperature (in °C or K)
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Identify the values:
- \( m = 6.00 , \text{g} \)
- \( c = 4.18 , \text{J/g-K} \)
- Initial temperature \( T_i = 20.0 , \text{°C} \)
- Final temperature \( T_f = 44.1 , \text{°C} \)
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Calculate the change in temperature \( \Delta T \): \[ \Delta T = T_f - T_i = 44.1 , \text{°C} - 20.0 , \text{°C} = 24.1 , \text{°C} \]
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Substitute the values into the formula: \[ q = 6.00 , \text{g} \cdot 4.18 , \text{J/g-K} \cdot 24.1 , \text{K} \]
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Calculate \( q \): \[ q = 6.00 \cdot 4.18 \cdot 24.1 \] \[ q = 6.00 \cdot 4.18 \approx 25.08 \] \[ q \approx 25.08 \cdot 24.1 \approx 604.41 , \text{J} \]
Thus, the amount of heat needed to raise the temperature of 6.00 g of water from 20.0 °C to 44.1 °C is approximately 604.4 joules.