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

First, understand the relationship between calories and energy. 1 kcal (kilocalorie) is equivalent to 1000 calories, and it is also equivalent to 4184 joules. Therefore, 500 kcal is equal to 500 * 4184 joules.

Next, recognize that the specific heat capacity of water is approximately 4.184 J/g°C. This means it takes 4.184 joules to raise the temperature of 1 gram of water by 1°C.

Calculate the total mass of the water. Since 1 liter of water weighs about 1 kg, a 50-L container of water would weigh approximately 50 kg, which is equivalent to 50,000 grams.

Use the formula for heat transfer: \( Q = m \, c \, \Delta T \), where \( Q \) is the heat energy in joules, \( m \) is the mass in grams, \( c \) is the specific heat capacity, and \( \Delta T \) is the change in temperature in °C. Rearrange the formula to solve for \( \Delta T \): \( \Delta T = \frac{Q}{m \, c} \).

Substitute the values into the formula: \( \Delta T = \frac{500 \, \text{kcal} \, \times \, 4184 \, \text{J/kcal}}{50,000 \, \text{g} \, \times \, 4.184 \, \text{J/g°C}} \). Calculate \( \Delta T \) to find the approximate increase in temperature of the water.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Calorimetry

Calorimetry is the science of measuring the heat of chemical reactions or physical changes. It involves using a calorimeter to determine the heat transfer between substances. In this context, it helps calculate how much heat from burning the pizza can increase the temperature of water, using the formula Q = mcΔT, where Q is heat energy, m is mass, c is specific heat capacity, and ΔT is the change in temperature.

Specific Heat Capacity

Specific heat capacity is the amount of heat required to change 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 the temperature change in the water when a known amount of heat is applied, as it determines how much energy is needed to raise the temperature of the water.

Energy Conversion

Energy conversion involves transforming energy from one form to another, such as chemical energy in food to thermal energy. In this scenario, the pizza's caloric content (500 kcal) is converted into heat energy. Knowing that 1 kcal equals 4184 joules allows us to calculate the total energy available to heat the water, which is essential for determining the temperature increase.