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

This is a weighted average problem: the moist soil is really two materials mixed together, dry soil and water, each with its own specific heat, and we need the combined specific heat of the mixture.

1. Set the basis: Since soil moisture is normally reported relative to dry soil mass, take 100 g of dry soil as the base. A 20% moisture content then means 20 g of water is mixed with that 100 g of dry soil.
2. Find each part's heat capacity: The dry soil part holds 100 g times its specific heat of 0.2, which is 20 heat units. The water part holds 20 g times its specific heat of 1.0, which is 20 heat units.
3. Add up the sample: Total mass of the moist sample is 100 g plus 20 g, that is 120 g, and total heat capacity is 20 plus 20, that is 40 heat units.
4. Divide to get specific heat: Specific heat of the moist soil is total heat capacity over total mass, 40 divided by 120, which works out to 0.333, rounding to 0.33.
5. Fix the unit: Specific heat is defined per unit mass in grams in this kind of problem. A value quoted per kilogram would be one thousand times smaller, nowhere near the listed choices, so the unit here has to be cal per gram.

Putting the number and the unit together, the specific heat of the moist soil sample comes out to 0.33 cal/g.

Let's summarize:

• Mixture specific heat is a mass weighted average of the parts.
• Soil moisture is read on a dry soil basis, so 20% means 20 g water per 100 g dry soil, giving 120 g total.

So the final answer is 0.33 cal/g.