Understanding Calorimetry: Calculating the Final Temperature of a Coffee Mixture

Are you a coffee lover like Mandie? If so, you might want to know how to mix different temperatures of water to create the perfect brewing temperature for your beloved beverage. In this article, we will explore the principle of calorimetry to calculate the final temperature of a coffee mixture that Mandie is preparing.

The Problem at Hand

Mandie is a coffee enthusiast who wants to prepare a perfect cup of coffee. He starts with 200 grams of hot water at a temperature of 80°C and mixes it with 100 grams of water at 15°C. Your task is to determine the final temperature of the mixture so that Mandie can enjoy his coffee while sipping it comfortably.

The Principle of Calorimetry

Calorimetry is the study of heat transfer, and it is based on the principle that heat lost by one object is equal to the heat gained by another. In terms of a mathematical equation, it can be represented as:

Heat lost Heat gained

Setting Up the Equation

Let's denote the final temperature of the mixture as T, and the specific heat of water as C. The formula we will use to calculate the final temperature is:

$$200 times C times 80 - T 100 times C times T - 15$$

Rewriting the equation for clarity, we get:

$$200 times 80 - T 100 times T - 15$$

Solving for the Final Temperature

Now, let's solve for T step by step:

First, simplify the equation: 16000 - 200T 100T - 1500 Next, combine like terms by adding 200T to both sides and adding 1500 to both sides: 300T 17500 Finally, divide both sides by 300 to solve for T: $$T frac{17500}{300} approx 58.33$$

Thus, the final temperature of the mixture is approximately 58.33°C.

Conclusion

By understanding the principle of calorimetry, we can accurately determine the final temperature of Mandie's coffee mixture. This calculation is crucial for coffee lovers who value the perfect brewing temperature for their favorite beverage. Whether you are a seasoned barista or a casual coffee drinker, knowing how to achieve the right temperature will enhance your enjoyment of your coffee.

Remember, the principle of calorimetry applies to various scenarios beyond just making coffee. It can be used in the food industry, manufacturing, and even in scientific research. It's a valuable tool to understand in the field of thermodynamics.

Happy sipping!