Calorie to Joule Conversion
Energy can be measured in various units, and understanding how to convert between these units is crucial in scientific calculations. One common conversion in nutrition and physics is between Calories and joules. Nutritional Calories, often denoted with an uppercase 'C', are actually kilocalories (kcal). This means that 1 Calorie is equivalent to 1000 small calories. To convert Calories into smaller, regular calories, you simply multiply by 1000. For instance, as in the example, if a donut contains 350 Calories, this is equivalent to 350,000 calories.
With calories obtained, the next task is to convert these into joules, the SI unit of energy. The conversion factor needed here is that 1 calorie is equal to 4.184 joules. Multiplying the number of calories by 4.184 gives the energy value in joules. So, 350,000 calories converts to 1,464,400 joules, helping us understand the energy content in a metric system context.
Converting between these units allows for better integration and comprehension when working with different scientific data, thus enabling more straightforward comparison and utilization across disciplines.
Specific Heat Capacity of Water
The specific heat capacity of a substance indicates how much energy is needed to change its temperature. For water, this capacity is famously high, specifically 4.184 joules per gram per degree Celsius (J/g°C). This means to increase the temperature of 1 gram of water by 1°C, 4.184 joules of energy are required.
This property makes water an excellent substance for thermal regulation and a benchmark for comparing the heat capacities of other materials. In practical applications, such as the exercise in question, knowing the specific heat capacity of water allows us to calculate the energy required to cause specific temperature changes, given a mass of water.
Using this value, you can determine the temperature increase of larger masses of water. When caloric energy, such as that from food or fuel, is converted and applied to heat water, the specific heat capacity ensures we can calculate how much that energy will raise the temperature of a given quantity of water, which is vital for both culinary applications and scientific calculations.
Temperature Change Calculation
Once the energy in joules and the specific heat capacity are known, calculating the temperature change of water becomes straightforward. The calculation uses the formula:
\( q = mc\Delta T \)
where \( q \) is the amount of energy in joules, \( m \) is the mass of water in grams, \( c \) is the specific heat capacity, and \( \Delta T \) is the temperature change in degrees Celsius.
First, ensure that the mass of water is in grams, as specific heat capacity is typically in J/g°C. In the given problem, with water weighing 35.5 kg, we convert this to grams: 35,500 grams. Using the specific heat capacity of water, 4.184 J/g°C, and the available energy from the donut, 1,464,400 J, we solve for \( \Delta T \). By rearranging the formula to find \( \Delta T \), it becomes:
\[ \Delta T = \frac{q}{mc} \]
Substituting the given values, the result is that the water temperature will increase by approximately 9.69°C. This formula not only helps when working with energy problems but also underscores the interplay between energy, mass, and temperature which is fundamental in thermodynamics.
