Question

Using the following data, calculate the kilocalories for each food burned in a calorimeter: a. I cup of popcorn that heats \(1250 \mathrm{~g}\) of water from \(25.5^{\circ} \mathrm{C}\) to \(50.8^{\circ} \mathrm{C}\) b. a sample of butter that heats \(357 \mathrm{~g}\) of water from \(22.7^{\circ} \mathrm{C}\) to \(38.8^{\circ} \mathrm{C}\)

Short answer

31.625 kcal for popcorn, 5.7477 kcal for butter.

Step-by-step solution

Identify the given data for popcorn

For the popcorn, the mass of the water is 1250 g, the initial temperature is 25.5°C and the final temperature is 50.8°C.

Calculate the temperature change for popcorn

Subtract the initial temperature from the final temperature: \( \text{Temperature change} = 50.8 °C - 25.5 °C = 25.3 °C \).

Compute the energy absorbed by water for popcorn

Use the formula \( Q = mc\triangle T \), where \( Q \) is energy in calories, \( m \) is mass, \( c \) is the specific heat capacity (1 cal/g°C for water), and \( \triangle T \) is the temperature change: \( Q = 1250 \text{ g} \times 1 \text{ cal/g°C} \times 25.3 °C = 31625 \text{ cal} \).

Convert calories to kilocalories for popcorn

Since 1 kilocalorie = 1000 calories, \( \text{Kilocalories} = \frac{31625 \text{ cal}}{1000} = 31.625 \text{ kcal} \).

Identify the given data for butter

For the butter, the mass of the water is 357 g, the initial temperature is 22.7°C and the final temperature is 38.8°C.

Calculate the temperature change for butter

Subtract the initial temperature from the final temperature: \( \text{Temperature change} = 38.8 °C - 22.7 °C = 16.1 °C \).

Compute the energy absorbed by water for butter

Use the formula \( Q = mc\triangle T \): \( Q = 357 \text{ g} \times 1 \text{ cal/g°C} \times 16.1 °C = 5747.7 \text{ cal} \).

Convert calories to kilocalories for butter

Since 1 kilocalorie = 1000 calories, \( \text{Kilocalories} = \frac{5747.7 \text{ cal}}{1000} = 5.7477 \text{ kcal} \).

Key concepts

specific heat capacity

Specific heat capacity is an essential concept in calorimetry. It is the amount of energy required to raise the temperature of one gram of a substance by one degree Celsius. In our exercise, water is the substance of interest, with a specific heat capacity of 1 cal/g°C. This value is vital because it allows us to calculate the energy absorbed or released during temperature changes. Remember, each substance has its own specific heat capacity, influencing how much energy is needed to change its temperature.

temperature change

Temperature change is crucial in calorimetry calculations. It's the difference between the initial and final temperatures of the substance being heated or cooled. For instance, when calculating the kilocalories of popcorn, we found the temperature change by subtracting the initial temperature (25.5°C) from the final temperature (50.8°C), resulting in a 25.3°C increase. Similarly, in the butter example, the temperature change was 16.1°C. The larger the temperature change, the more energy is involved in the process.

energy conversion

Energy conversion is a key concept when dealing with calorimetry. Energy is typically measured in calories, but to make values more manageable, we often convert them to kilocalories. In our example with popcorn, the energy calculated was 31,625 calories. By dividing by 1,000 (since 1 kilocalorie equals 1,000 calories), we converted this into 31.625 kilocalories. This conversion helps to simplify and compare large energy values easily.

energy absorbed by water

The energy absorbed by water is a pivotal point in calorimeter exercises. When a substance releases energy, often this energy is transferred to water, causing its temperature to rise. We calculate this energy using the formula: \( Q = mc\Delta T \). Here, \( Q \) represents energy in calories, \( m \) is the mass of water, \( c \) is the specific heat capacity, and \( \Delta T \) is the temperature change. For the popcorn example, the mass was 1250 g, specific heat capacity was 1 cal/g°C, and temperature change was 25.3°C, yielding 31,625 calories of energy absorbed. By understanding this process, we can quantify the energy content in different foods.