How many Btus are required to change five pounds of water at 40°F to  200°F?

specific heat of ice =  0.5 

specific heat of water  = 1.0 

specific heat of steam = 0.5 

latent heat of melting = 144 

latent heat of boiling = 970 

Group of answer choices

1600 Btu

800 Btu

400 Btu

200 Btu

To calculate the amount of heat (in Btu) required to change 5 pounds of water from 40°F to 200°F, we will use the formula for sensible heat:

\[
Q = m \cdot c \cdot \Delta T
\]

Where:
- \( Q \) is the heat required (in Btu),
- \( m \) is the mass of water (in pounds),
- \( c \) is the specific heat of water (Btu/lb/°F),
- \( \Delta T \) is the change in temperature (in °F).

### Step 1: Identifying the temperature change
The temperature change (\( \Delta T \)) is from 40°F to 200°F:

\[
\Delta T = 200°F - 40°F = 160°F
\]

### Step 2: Applying the formula
Given that the specific heat of water \( c = 1.0 \, \text{Btu/lb/°F} \) and the mass of water is 5 pounds, we can calculate the total heat required to raise the temperature.

\[
Q = 5 \, \text{lb} \times 1.0 \, \text{Btu/lb/°F} \times 160 \, \text{°F}
\]
\[
Q = 800 \, \text{Btu}
\]

Thus, **800 Btu** is required to heat the 5 pounds of water from 40°F to 200°F.

### Final Answer:
The correct answer is **800 Btu**.

Would you like any further details or explanations on this? 

Here are some related questions to expand on this topic:
1. How much heat would be required to boil the water at 200°F?
2. What if we had started with ice at 32°F—how much heat would be needed to reach 200°F?
3. How does the latent heat of boiling affect the total heat required when converting water to steam?
4. What is the difference between sensible heat and latent heat?
5. How would the heat requirement change if we were dealing with steam instead of water?

**Tip:** Always remember that the specific heat of a substance changes depending on whether it's in solid, liquid, or gaseous form.

How many Btus are required to change five pounds of water at 40°F to 200°F?

Learn how to calculate the BTUs required to change 5 pounds of water from 40°F to 200°F using the specific heat capacity formula. This problem demonstrates heat transfer concepts in thermodynamics, making it ideal for high school students in Grades 10-12.

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