Problem 5 - University Physics with Modern Physics

Question

You put a bottle of soft drink in a refrigerator and leave it until its temperature has dropped 10.0 K. What is its temperature change in (a) F\(^\circ\) and (b) C\(^\circ\)?

Step-by-Step Solution

Answer

10.0 K equals 10.0 C° and 18.0 F° temperature change.

Step 1: Understand the Problem

The problem provides a temperature change in Kelvin (10.0 K) and asks us to convert this change to Fahrenheit and Celsius.

Step 2: Convert Kelvin Change to Celsius Change

Since a change of 1 Kelvin is equivalent to a change of 1 degree Celsius, a temperature change of 10.0 K is equal to a change of 10.0 °C.

Step 3: Convert Celsius Change to Fahrenheit Change

Use the conversion formula for temperature differences: \( \Delta T_{°F} = \Delta T_{°C} \times \frac{9}{5} \). Substitute \( \Delta T_{°C} = 10.0 \) to get \( \Delta T_{°F} = 10.0 \times \frac{9}{5} = 18.0 \).

Step 4: Conclusion

The temperature change in Fahrenheit is 18.0 F° and in Celsius is 10.0 C°.

Key Concepts

Kelvin to Celsius

The Kelvin and Celsius scales are two fundamental ways to measure temperature. A remarkable feature of these two scales is how closely they relate to each other.
To convert a temperature difference from Kelvin to Celsius, there is actually nothing complex about it. This is because both scales increase at the same rate.

• 1 degree Celsius is exactly equal to 1 Kelvin when it comes to a temperature change.

This means that if an object experiences a temperature change of 10.0 Kelvin, its change in degrees Celsius would also be 10.0 C°.
This direct equivalence makes calculations between Kelvin and Celsius very straightforward. There's no need to add or subtract any constant—just a simple 1-to-1 conversion!

Celsius to Fahrenheit

Sometimes, you need to express Celsius in Fahrenheit, especially in places where Fahrenheit is commonly used.
When dealing with temperature changes, the scale conversion requires a little formulaic adjustment.To convert a temperature difference from Celsius to Fahrenheit, use the formula:\[ \Delta T_{°F} = \Delta T_{°C} \times \frac{9}{5} \]This equation scales the Celsius change into Fahrenheit.
For example, if a temperature change is 10.0 °C, then:

• Plug into the formula: \(\Delta T_{°F} = 10.0 \times \frac{9}{5} = 18.0\)
• The temperature change is 18.0 Fahrenheit degrees (F°).

This conversion is essential for countless scientific, engineering, and everyday practical applications, ensuring everyone can understand and communicate temperature changes efficiently.

Temperature Change

Temperature change refers to how much the temperature of an object or substance increases or decreases.
This is an essential concept in physics and everyday life because it affects how substances react or behave.Here are a few things to note about temperature changes:

• Temperature change can occur in various scales such as Kelvin, Celsius, or Fahrenheit.
• It is represented by the symbol \(\Delta T\), where \(\Delta\) signifies change.
• It's crucial for understanding environmental shifts, chemical reactions, and physical transformations.

Whether you're chilling a beverage or studying thermodynamics, knowing how to properly calculate and express temperature changes helps you grasp the broader implications of heat transfer and energy conversion.