The amount of moisture that must evaporate from a 5.0 kg body to reduce its temperature by 2°C is \( m \) g. The heat of vaporization for water at body temperature is about 580 cal/g. The specific heat capacity for the body is 0.83 cal/g°C. The value of \( m \) is:

Question

Which is an adiabatic process?

Answer 1

Step 1: Find the heat the body loses.
The body has mass 5.0 kg = 5000 g, specific heat capacity 0.83 cal/g°C, and drops by 2°C. The heat lost is:
\[ Q = mc\Delta T = 5000 \times 0.83 \times 2 = 8300\,\text{cal} \]

Step 2: Set that heat equal to the heat carried off by evaporating moisture.
Each gram of moisture that evaporates carries away 580 cal, so \( m \) grams carry away:
\[ Q_{\text{evap}} = 580m \]

Step 3: Equate and solve for m.
\[ 580m = 8300 \]
\[ m = \frac{8300}{580} \approx 14.31\,\text{g} \]

Step 4: Final Answer.
\[ \boxed{m \approx 14.3\,\text{g}} \]

Answer 2

Instead of computing the total heat lost first, this method compares the two heat quantities as a direct ratio, which cancels out the mass unit and gets straight to the fraction of mass that must evaporate.

14.3 g: The heat lost per gram of body mass for a 2°C drop is \( 0.83 \times 2 = 1.66 \) cal/g. Dividing this by the 580 cal/g needed to evaporate each gram of moisture gives the fraction of the body's mass that must evaporate: \( \frac{1.66}{580} \approx 0.002862 \). Applying that fraction to the body's 5000 g gives \( 5000 \times 0.002862 \approx 14.3 \) g.
19.5 g: This would need a fraction of about \( \frac{19.5}{5000} = 0.0039 \), noticeably higher than the 0.002862 the ratio actually gives.
25.4 g: This corresponds to a fraction near 0.00508, close to double what the ratio calculation supports.
35.2 g: This corresponds to a fraction near 0.00704, more than double the actual fraction, making it the furthest off of the four.

Working with the ratio of specific heat effect to latent heat directly (1.66 cal/g against 580 cal/g) shows that only a small slice, about 0.29 percent, of the body's mass needs to evaporate, which comes to about 14.3 g for a 5000 g body.

The correct answer is 14.3 g.

Answer 3

Instead of computing the total heat lost first, this method compares the two heat quantities as a direct ratio, which cancels out the mass unit and gets straight to the fraction of mass that must evaporate.

14.3 g: The heat lost per gram of body mass for a 2°C drop is \( 0.83 \times 2 = 1.66 \) cal/g. Dividing this by the 580 cal/g needed to evaporate each gram of moisture gives the fraction of the body's mass that must evaporate: \( \frac{1.66}{580} \approx 0.002862 \). Applying that fraction to the body's 5000 g gives \( 5000 \times 0.002862 \approx 14.3 \) g.
19.5 g: This would need a fraction of about \( \frac{19.5}{5000} = 0.0039 \), noticeably higher than the 0.002862 the ratio actually gives.
25.4 g: This corresponds to a fraction near 0.00508, close to double what the ratio calculation supports.
35.2 g: This corresponds to a fraction near 0.00704, more than double the actual fraction, making it the furthest off of the four.

Working with the ratio of specific heat effect to latent heat directly (1.66 cal/g against 580 cal/g) shows that only a small slice, about 0.29 percent, of the body's mass needs to evaporate, which comes to about 14.3 g for a 5000 g body.

The correct answer is 14.3 g.

The amount of moisture that must evaporate from a 5.0 kg body to reduce its temperature by 2°C is \( m \) g. The heat of vaporization for water at body temperature is about 580 cal/g. The specific heat capacity for the body is 0.83 cal/g°C. The value of \( m \) is:

Show Hint

The Correct Option is B

Approach Solution - 1

Approach Solution -2

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