Calculate the number of btu’s required to change 741 lbs of steam at 275 degrees to 741lbs of ice at 22 degrees

To solve this problem, we need to calculate the energy required to cool and change the state of 741 pounds of steam at 275°F into ice at 22°F. The process involves multiple steps as the steam undergoes both temperature changes and phase changes. Let's break it down:

### Steps:

1. **Cool the steam from 275°F to 212°F (boiling point of water).**
2. **Condense the steam at 212°F to water at 212°F.**
3. **Cool the water from 212°F to 32°F (freezing point of water).**
4. **Freeze the water at 32°F into ice.**
5. **Cool the ice from 32°F to 22°F.**

We will use the following constants:
- **Specific heat of steam:** 0.48 BTU/lb°F
- **Latent heat of vaporization (steam to water):** 970.3 BTU/lb
- **Specific heat of water:** 1.0 BTU/lb°F
- **Latent heat of fusion (water to ice):** 144 BTU/lb
- **Specific heat of ice:** 0.5 BTU/lb°F

### 1. Cool the steam from 275°F to 212°F:
\[
\text{BTU} = m \cdot c \cdot \Delta T = 741 \cdot 0.48 \cdot (275 - 212) = 741 \cdot 0.48 \cdot 63 = 22433.76 \text{ BTU}
\]

### 2. Condense the steam at 212°F into water at 212°F:
\[
\text{BTU} = m \cdot \text{latent heat of vaporization} = 741 \cdot 970.3 = 718892.3 \text{ BTU}
\]

### 3. Cool the water from 212°F to 32°F:
\[
\text{BTU} = m \cdot c \cdot \Delta T = 741 \cdot 1.0 \cdot (212 - 32) = 741 \cdot 180 = 133380 \text{ BTU}
\]

### 4. Freeze the water at 32°F into ice:
\[
\text{BTU} = m \cdot \text{latent heat of fusion} = 741 \cdot 144 = 106704 \text{ BTU}
\]

### 5. Cool the ice from 32°F to 22°F:
\[
\text{BTU} = m \cdot c \cdot \Delta T = 741 \cdot 0.5 \cdot (32 - 22) = 741 \cdot 0.5 \cdot 10 = 3705 \text{ BTU}
\]

### Total Energy Required:

\[
\text{Total BTU} = 22433.76 + 718892.3 + 133380 + 106704 + 3705 = 984115.06 \text{ BTU}
\]

### Final Answer:
The total number of BTU required is **984,115 BTU**.

Would you like more details or have any questions?

Here are some related questions to consider:
1. How do phase changes impact energy calculations in heating or cooling processes?
2. What is the difference between latent heat and specific heat?
3. How would this problem change if the steam were initially at a higher temperature?
4. Can you explain how specific heat varies for different states of matter?
5. What are the units of BTU, and how do they relate to other energy units like joules?

**Tip:** When dealing with phase changes, always account for both the temperature change and the latent heat during state transitions.

Calculate the number of BTU’s required to change 741 lbs of steam at 275 degrees to 741 lbs of ice at 22 degrees.

Discover how to calculate the number of BTUs required to convert 741 pounds of steam at 275°F to ice at 22°F through step-by-step thermodynamic calculations. Learn about phase changes, specific heat, latent heat, and energy conversion formulas, suitable for advanced learners in thermodynamics.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation