When 1.0 tablespoon of butter is burned or used by our body, it releases 100 kcal (100 food Calories or 418. 4 kJ) of energy. If we could use all the energy provided, how many tablespoons of butter would have to be burned to raise the temperature of 3.00 L of water from 18.0 ℃ to 90.0 ℃

Verified step by step guidance

1. Calculate the temperature change (\( \Delta T \)) of the water by subtracting the initial temperature from the final temperature: \( \Delta T = 90.0 \, ^\circ\text{C} - 18.0 \, ^\circ\text{C} \).
2. Use the specific heat capacity formula to calculate the energy required to raise the temperature of the water: \( q = m \cdot c \cdot \Delta T \), where \( q \) is the heat energy, \( m \) is the mass of the water, \( c \) is the specific heat capacity of water (4.184 J/g°C), and \( \Delta T \) is the temperature change.
3. Convert the volume of water from liters to grams, knowing that the density of water is approximately 1 g/mL, so 3.00 L of water is equivalent to 3000 g.
4. Substitute the values into the specific heat capacity formula to find the total energy required in joules.
5. Convert the energy required from joules to kilocalories, knowing that 1 kcal = 4184 J, and then determine how many tablespoons of butter are needed by dividing the total energy required in kilocalories by the energy provided by one tablespoon of butter (100 kcal).

Key Concepts

Specific Heat Capacity

Specific heat capacity is the amount of heat required to raise the temperature of a unit mass of a substance by one degree Celsius. For water, this value is approximately 4.18 J/g°C. Understanding this concept is crucial for calculating how much energy is needed to change the temperature of water, as it directly relates to the mass of water and the temperature change involved.

Energy Conversion

Energy conversion refers to the process of changing energy from one form to another. In this context, the energy released from burning butter (in kcal) must be converted to joules to match the units used for calculating the heat required to raise the temperature of water. Knowing how to convert between these units is essential for solving the problem accurately.

Calorimetry

Calorimetry is the science of measuring the heat of chemical reactions or physical changes. In this scenario, it involves calculating the total energy needed to heat a specific volume of water from one temperature to another. By applying the principles of calorimetry, one can determine how many tablespoons of butter must be burned to provide the necessary energy to achieve the desired temperature change.