Question

After a week, biochemical reactions in compost slow, and the temperature drops to \(45^{\circ} \mathrm{C}\). The dark brown organic-rich mixture is ready for use in the garden. What is this temperature in Fahrenheit degrees? In kelvins?

Short answer

The temperature is \(113^{\circ}F\) and 318.15 K.

Step-by-step solution

- Understand the Temperature Conversion Formulas

To convert Celsius to Fahrenheit, use the formula: \[ F = \frac{9}{5}C + 32 \]To convert Celsius to Kelvins, use the formula:\[ K = C + 273.15 \]

- Convert Celsius to Fahrenheit

Substitute the given temperature (\[ C = 45^{\circ}C \]) into the Fahrenheit formula:\[ F = \frac{9}{5} \times 45 + 32 = 81 + 32 = 113^{\circ}F \]

- Convert Celsius to Kelvins

Substitute \( C = 45^{\circ}C \) into the Kelvin formula:\[ K = 45 + 273.15 = 318.15 \text{ K} \]

Key concepts

Celsius to Fahrenheit conversion

The Celsius (°C) and Fahrenheit (°F) scales are two of the most commonly used temperature scales. To convert a temperature from Celsius to Fahrenheit, you use the formula \( F = \frac{9}{5}C + 32 \). This formula helps us translate the temperature measured on the Celsius scale into the Fahrenheit scale.

For example, if the temperature in your compost is \( 45^{\text{°}C} \), you can convert it into Fahrenheit by substituting this value into the formula. First, multiply 45 by 9, then divide the result by 5. That gives you 81.

After that, you add 32 to 81, resulting in 113. So, \( 45^{\text{°}C} \) becomes \( 113^{\text{°}F} \). This is how you convert Celsius to Fahrenheit step by step.

Celsius to Kelvin conversion

Converting Celsius to Kelvin is a bit more straightforward but equally important, especially in scientific contexts. The Kelvin scale (\text{K}\text{)}) is an absolute temperature scale with its zero point at absolute zero, the lowest possible temperature where all molecular motion stops.

To convert Celsius to Kelvin, you simply add 273.15 to the Celsius temperature. This is because zero degrees Celsius is equivalent to 273.15 Kelvins. The formula you use is \( K = C + 273.15 \).

So, if the compost’s temperature is \( 45^{\text{°}C} \), you add 273.15 to get \( 318.15 \text{K} \). This conversion process ensures that we can relate temperature changes directly, whether using the Celsius or Kelvin scale.

biochemical reactions in compost

Biochemical reactions play a crucial role in composting. These reactions break down organic materials into simpler compounds that enrich the soil. When you start a compost pile, various microorganisms like bacteria and fungi get to work breaking down materials.

This degradation process releases heat, causing the temperature of the compost to rise. In the first few days, the temperature can go as high as \( 70^{\text{°}C} \), indicating vigorous microbial activity.

As the easily degradable materials are consumed, the temperature starts to drop. After a week or so, you might notice a significant reduction in temperature, down to about \( 45^{\text{°}C} \). This drop suggests that the compost is moving into a maturation phase.

At this point, the dark brown organic mixture is almost ready for use, providing nutrient-rich matter to enhance your garden's soil. Understanding temperature changes in composting helps you ensure the process is going smoothly and efficiently.