The specific heat of soil is 0.20 kcal/kgC and the specific heat of water is 1.00 kcal/kgC. This means that if 1 kg of soil and 1 kg of water each receive 1 kcal of energy, id…

Question

asked Jan 5, 2020 121k views

1 Answer

Harald Hoyer · Answer 1 · 2020-01-11T04:31:21+0000

Answer: The soil will be
$4\°C$ warmer than the water.

Step-by-step explanation:

The heat (thermal energy) absorbed can be found using the following equation:

$Q=m.C.\Delta T$

Where:

is the heat

is the mass of the element

is the specific heat capacity of the material.

$\Delta T$ is the variation in temperature

In the case of soil we have:

$Q_(soil)=m_(soil).C_(soil).\Delta T_(soil)$ (1)

Where:

Q_(soil)=1 kcal

m_(soil)=1 kg

$C_(soil)=0.2 kcal/kg \°C$

$\Delta T_(soil)$

In the case of water we have:

$Q_(water)=m_(water).C_(water).\Delta T_(water)$ (2)

Where:

Q_(water)=1 kcal

m_(water)=1 kg

$C_(water)=1 kcal/kg \°C$

$\Delta T_(water)$

Isolating
$\Delta T$ from both equations:

$\Delta T_(soil)=(Q_(soil))/(m_(soil).C_(soil))$ (3)

$\Delta T_(soil)=(1 kcal)/(1 kg(0.2 kcal/kg \°C))$

$\Delta T_(soil)=5\°C$ (4)

$\Delta T_(water)=(Q_(water))/(m_(water).C_(water))$ (5)

$\Delta T_(water)=(1 kcal)/(1 kg(1 kcal/kg \°C))$

$\Delta T_(water)=1\°C$ (6)

Comparing (4) and (6) we can find the soil will be
$4\°C$ warmer than the water.