Question

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

Answer 1

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

Explanation:

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

$Q=m.C.\Delta T$

Where:

$Q$ is the heat  

$m$ is the mass of the element

$C$ 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:

$\Delta T_{soil}=\frac{Q_{soil}}{m_{soil}.C_{soil}}$ (3)

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

$\Delta T_{soil}=5\°C$ (4)

$\Delta T_{water}=\frac{Q_{water}}{m_{water}.C_{water}}$ (5)

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

$\Delta T_{water}=1\°C$ (6)

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