48. PHYSICAL SCIENCE

To convert temperature from degrees Celsius (C) to kelvins (K), the formula [tex]K = C + 273[/tex] is used.

a. If chlorine is frozen when [tex]K < 172[/tex], what temperatures in degrees Celsius will guarantee that the chlorine stays frozen?

b. If nitrogen is frozen when [tex]C < -210[/tex], what temperatures in kelvins will guarantee that the nitrogen stays frozen?

Sure! Let's break down the solution to the given question step-by-step.

### Part a: Chlorine Freezing Point

We need to determine the temperatures in degrees Celsius that will guarantee chlorine stays frozen.

1. We are given that chlorine stays frozen when the temperature in Kelvins (K) is less than 172.
2. The formula to convert Celsius (C) to Kelvins (K) is [tex]\( K = C + 273 \)[/tex].

Using this formula, we can convert the freezing point from Kelvins to Celsius:

[tex]\[
172 = C + 273
\][/tex]

3. To solve for [tex]\( C \)[/tex], subtract 273 from both sides of the equation:

[tex]\[
C = 172 - 273
\][/tex]

[tex]\[
C = -101
\][/tex]

So, chlorine will stay frozen at temperatures below -101 degrees Celsius.

### Part b: Nitrogen Freezing Point

We need to determine the temperatures in Kelvins that will guarantee nitrogen stays frozen.

1. We are given that nitrogen stays frozen when the temperature in Celsius (C) is less than -210.
2. Using the same conversion formula, we can convert the freezing point from Celsius to Kelvins:

[tex]\[
K = -210 + 273
\][/tex]

3. Solve for [tex]\( K \)[/tex]:

[tex]\[
K = 63
\][/tex]

So, nitrogen will stay frozen at temperatures below 63 Kelvins.

### Summary:

- a. Chlorine stays frozen at temperatures below -101 degrees Celsius.
- b. Nitrogen stays frozen at temperatures below 63 Kelvins.

I hope this clarifies how to solve the problem! If you have any more questions, feel free to ask.