# How much heat is required to warm 1.60 kg of sand from 22°C to 100°C?

May 3, 2016

The energy required to heat the sand by ${78}^{\circ} \text{C}$ is $\approx$$\text{36000 J}$.

#### Explanation:

The specific heat capacity for sand, $c$, is $\text{0.290 J/g"^@"C}$.
http://www2.ucdsb.on.ca/tiss/stretton/database/Specific_Heat_Capacity_Table.html

The equation for determining the heat required to increase the temperature of the sand is $Q = c m \Delta T$, where $Q$ is heat energy in Joules, $m$ is mass in grams, $c$ is specific heat capacity, and $\Delta T$ is the change in temperature, $\left({T}_{\text{final"-T_"initial}}\right)$.

Delta T=(100^@"C")-(22^@"C")=78^@"C"

Mass of sand in grams:

$1.60 \cancel{\text{kg"xx(1000"g")/(1cancel"kg")="1600 g}}$

Substitute the given values into the equation.

Q=(0.290"J/g"^@"C")xx(1600"g")xx(78^@"C")="36000 J" (rounded to two significant figures)