Problem 13 - Chemistry: Principles and Reactions

Question

A glass of lukewarm milk is suggested for people who cannot sleep. Milk at \(52^{\circ} \mathrm{C}\) can be characterized as lukewarm. What is the temperature of lukewarm milk in \({ }^{\circ} \mathrm{F}\) ? In \(\mathrm{K}\) ?

Step-by-Step Solution

Answer

Answer: The temperature of lukewarm milk is 125.6°F in Fahrenheit and 325.15K in Kelvin.

Step 1: Convert Celsius to Fahrenheit

Using the formula for converting Celsius to Fahrenheit: \(F = \frac{9}{5}C + 32\) First, we will plug the given temperature in Celsius, \(52^{\circ} \mathrm{C}\), into the formula: \(F = \frac{9}{5}(52) + 32\) Now, we will calculate the value for Fahrenheit: \(F = 93.6 + 32 = 125.6\) So, the temperature of lukewarm milk is \(125.6^{\circ} \mathrm{F}\).

Step 2: Convert Celsius to Kelvin

Using the formula for converting Celsius to Kelvin: \(K = C + 273.15\) Next, we will plug the given temperature in Celsius, \(52^{\circ} \mathrm{C}\), into the formula: \(K = 52 + 273.15\) Now, we will calculate the value for Kelvin: \(K = 325.15\) So, the temperature of lukewarm milk is \(325.15\mathrm{K}\). In conclusion, the lukewarm milk has a temperature of \(125.6^{\circ} \mathrm{F}\) in Fahrenheit and \(325.15\mathrm{K}\) in Kelvin.

Key Concepts

Celsius to Fahrenheit

The conversion from Celsius to Fahrenheit is a common task, especially when dealing with temperature differences in scientific and daily contexts. The formula to convert a temperature from degrees Celsius (°C) to degrees Fahrenheit (°F) is relatively straightforward:

• Use the formula: \[ F = \frac{9}{5} C + 32 \]

To better understand, let’s convert a specific temperature. For the case of lukewarm milk at \(52^{\circ} \mathrm{C}\), we substitute this value into the formula:

• Calculate: \[ F = \frac{9}{5}(52) + 32 \]
• This simplifies to: \[ F = 93.6 + 32 \]
• Resulting in: \[ F = 125.6 \]

Thus, \(52^{\circ} \mathrm{C}\) is equivalent to \(125.6^{\circ} \mathrm{F}\). The conversion tells us how temperatures increase between these scales due to different starting points and intervals used in each. While Celsius increments by 1 degree, Fahrenheit increments by 1.8 (or \(\frac{9}{5}\)). This is an essential concept to remember when comparing temperatures across different scales.

Celsius to Kelvin

When converting temperatures from Celsius to Kelvin, we simplify our understanding of absolute scales. Celsius and Kelvin are both metric systems, but Kelvin is the SI unit for temperature, making it crucial in scientific calculations. The formula for converting Celsius to Kelvin is simple:

• Use the formula: \[ K = C + 273.15 \]

Let's see how this works with the temperature of lukewarm milk at \(52^{\circ} \mathrm{C}\):

• Calculate: \[ K = 52 + 273.15 \]
• Which results in: \[ K = 325.15 \]

Thus, \(52^{\circ} \mathrm{C}\) equals \(325.15 \mathrm{K}\). Kelvin begins at absolute zero, or 0 K, which is \(273.15\) degrees less than 0°C. This scale is absolute as it starts from the theoretical point where particles have minimal thermal motion. This conversion reminds us that understanding temperature in Kelvin is often more practical in scientific contexts, especially in chemistry and physics. It provides consistency and clarity when analyzing thermodynamic equations and principles.

Temperature in Chemistry

Temperature plays a critical role in chemistry, influencing reaction rates, equilibrium, and states of matter. Understanding temperature scales, especially Celsius, Kelvin, and Fahrenheit, is key to translating experimental findings and standardizing results across scientific disciplines.

• Chemistry uses Kelvin heavily due to its absolute scale, which provides a consistent base for calculations. The Kelvin scale helps in defining concepts such as the ideal gas law and reaction dynamics.
• Celsius is also used in lab environments for its practical alignment with the Kelvin scale and ease of measurement.
• Temperature impacts reaction rates; typically, an increase in temperature increases the rate of reaction, aligning with the collision theory.

Comprehending these temperature scales and conversions ensures accurate experimental outcomes. It's particularly beneficial in thermodynamics, where precise measurements of thermal energy exchanges are necessary. Consistency in units helps make chemists' and physicists' work universal, improving reproducibility and comparability of experiments across different laboratories worldwide.