during a bout with a flu an 88kg man ran a fever of 40.84 degrees C instead of the normal body temperature. assuming that the human body is mostly water, how much heat(J) is required to raise his temperature by that amount? round off two decimal places.

To calculate the heat (in joules) required to raise the man's temperature, we can use the formula:

\[
Q = mc\Delta T
\]

Where:
- \( Q \) is the heat energy (in joules),
- \( m \) is the mass of the object (in kilograms),
- \( c \) is the specific heat capacity of water (since the body is mostly water), which is approximately \( 4186 \, \text{J/kg}^\circ\text{C} \),
- \( \Delta T \) is the change in temperature (in Celsius).

### Step 1: Calculate the change in temperature
The initial normal body temperature is 37.00°C, and the fever temperature is 40.84°C. So, the change in temperature \( \Delta T \) is:

\[
\Delta T = 40.84^\circ\text{C} - 37.00^\circ\text{C} = 3.84^\circ\text{C}
\]

### Step 2: Apply the formula
Now, using the formula \( Q = mc\Delta T \):
\[
Q = 88 \, \text{kg} \times 4186 \, \text{J/kg}^\circ\text{C} \times 3.84^\circ\text{C}
\]

Let me calculate that for you.The amount of heat required to raise the man's temperature by \( 3.84^\circ\text{C} \) is approximately \( 1,414,533.12 \, \text{J} \).

Would you like more details or have any questions? Here are five related questions to expand on this:

1. How does the specific heat of water compare to other substances?
2. What effect does body mass have on the heat required to change temperature?
3. How would this calculation change if the man's body were composed of substances other than water?
4. What would happen to the body if the heat were not properly dissipated?
5. How does the body regulate temperature during illness?

**Tip:** When dealing with temperature changes in everyday scenarios, using specific heat helps relate heat energy to practical effects like warming or cooling.

During a bout with the flu, an 88kg man ran a fever of 40.84°C instead of the normal body temperature. Assuming that the human body is mostly water, how much heat (J) is required to raise his temperature by that amount? Round off to two decimal places.

Learn how to calculate the heat energy required to raise an 88kg man's temperature from normal to 40.84°C using the specific heat capacity formula. This problem demonstrates concepts in thermodynamics and heat transfer, perfect for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation