A slice of pizza has 500 kcal. If we could burn the pizza and use all the heat to warm a 50-L container of cold water, what would be the approximate increase in the temperature of the water? (Note: A liter of cold water weighs about 1 kg.) a. 50°C b. 5°C c. 100°C d. 10°C

Verified step by step guidance

1. First, convert the energy from kilocalories to joules. Recall that 1 kcal = 4184 joules. Therefore, 500 kcal = 500 x 4184 joules = 2092000 joules.
2. Next, use the formula for heat transfer Q = mc\Delta T, where Q is the heat energy in joules, m is the mass of the water, c is the specific heat capacity of water (approximately 4184 J/kg\degree C), and \Delta T is the change in temperature.
3. Since the mass of the water (m) is approximately equal to the volume in liters for water (50 L = 50 kg), substitute the values into the formula: 2092000 J = 50 kg x 4184 J/kg\degree C x \Delta T.
4. Solve for \Delta T (change in temperature). Rearrange the formula to \Delta T = Q / (m x c). Substituting the values gives \Delta T = 2092000 J / (50 kg x 4184 J/kg\degree C) = 10\degree C.
5. Therefore, the approximate increase in the temperature of the water would be 10\degree C, which corresponds to answer choice d.

Key Concepts

Caloric Energy

Caloric energy is the amount of energy that food provides when consumed, measured in kilocalories (kcal). In this context, the slice of pizza contains 500 kcal, which can be converted into heat energy when burned. Understanding how this energy can be transferred to another substance, like water, is crucial for solving the problem.

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. This concept is essential for calculating how much the temperature of the water will increase when it absorbs the heat from the burned pizza.

Heat Transfer

Heat transfer refers to the movement of thermal energy from one object or substance to another. In this scenario, the heat generated from burning the pizza is transferred to the water, causing its temperature to rise. Understanding the principles of heat transfer helps in determining the final temperature of the water after absorbing the energy.