"6345 J" of energy are required to raise the temperature of water from 22.6^@"C" to 45.1^@"C". What is the mass of the water?

Apr 30, 2017

The mass of water is $\text{67.4 g}$.

Explanation:

Use the equation:

$q = m c \Delta t$

where $q$ is energy in Joules (J), $m$ is mass, $c$ is specific heat capacity, and $\Delta t$, which is change in temperature. $\Delta t = {T}_{\text{final"-T_"initial}}$

The specific heat capacity of water, ${c}_{\text{H2O}}$, is not given. It is 4.184 "J"/("g"*^@"C").
https://water.usgs.gov/edu/heat-capacity.html

Given
$q = \text{6345 J}$
c_"H2O"=4.184 "J"/("g"*^@"C")
Deltat=("45.1"^@"C"-"22.6"^@"C")="22.5"^@"C"

Unknown: mass in grams

Solution
Rearrange the equation to isolate $m$. Substitute the given values into the equation and solve.

$m = \frac{q}{c \Delta t}$

m=(6345color(red)cancel(color(black)("J")))/(4.184color(red)cancel(color(black)("J"))/("g"*^@color(red)cancel(color(black)("C")))xx22.5^@color(red)cancel(color(black)("C")))="67.4 g H"_2"O" (rounded to three significant figures)