Question

If a soil sample contains 20% moisture, calculate the specific heat of this soil (specific heat of water and soil is 1.0 and 0.2, respectively).

• A. 0.44 cal/kg
• B. 0.44 cal/g
• C. 0.33 cal/kg
• D. 0.33 cal/g

Hint:

Take moisture content on a dry soil weight basis, average the two specific heats by mass, and check which unit, cal/kg or cal/g, actually makes sense for a specific heat value.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
We need the specific heat of a moist soil sample that is a mixture of dry soil solids and water, given the specific heat of pure water as 1.0 and of dry soil as 0.2, with a moisture content of 20%.

Step 2: Key Formula or Approach:
The specific heat of a mixture is a weighted average of the specific heats of its parts, weighted by the mass of each part. In soil science, moisture content is conventionally expressed on a dry weight basis, meaning it is the mass of water divided by the mass of oven dry soil, not by the total wet mass. So a 20% moisture content means 20 g of water for every 100 g of dry soil.
\[ C_{mix} = \frac{M_{soil} \times C_{soil} + M_{water} \times C_{water}}{M_{soil} + M_{water}} \]

Step 3: Detailed Explanation:
Take a basis of 100 g of dry soil. At 20% moisture on a dry weight basis, the mass of water present is 20 g.
Total mass of the moist sample is 100 g soil plus 20 g water, which is 120 g.
Heat capacity contributed by the dry soil is 100 g times 0.2 cal per g, giving 20 cal per degree.
Heat capacity contributed by the water is 20 g times 1.0 cal per g, giving 20 cal per degree.
Total heat capacity of the moist sample is 20 plus 20, which is 40 cal per degree.
Specific heat of the moist soil, per gram, is this total heat capacity divided by the total mass:
\[ C_{mix} = \frac{40}{120} = 0.333\ \text{cal/g} \]
Rounding this gives 0.33 cal per gram, and since specific heat is naturally expressed per gram (a per kilogram value would be a thousand times smaller, around 0.00033, which does not match any listed option), the unit must be cal per gram.

Step 4: Final Answer:
The specific heat of the moist soil sample is 0.33 cal/g. \[ \boxed{0.33\ \text{cal/g}} \]