Question

what is the mass of a sample of mercury which absorbs 1210 j of energy when its temperature is increased by 15.4 °c?
(c_{hg} = 0.126 \frac{j}{g \cdot ^\circ c})

m = ? g

Explanation:

Step1: Recall the heat formula

The formula for heat absorbed or released is $q = mc\Delta T$, where $q$ is the heat energy, $m$ is the mass, $c$ is the specific heat capacity, and $\Delta T$ is the change in temperature. We need to solve for $m$, so rearrange the formula to $m=\frac{q}{c\Delta T}$.

Step2: Identify the given values

We know that $q = 1210\ J$, $c = 0.126\ \frac{J}{g\cdot^\circ C}$, and $\Delta T = 15.4\ ^\circ C$.

Step3: Substitute the values into the formula

Substitute the values into $m=\frac{q}{c\Delta T}$: $m=\frac{1210\ J}{0.126\ \frac{J}{g\cdot^\circ C}\times15.4\ ^\circ C}$.
First, calculate the denominator: $0.126\times15.4 = 1.9404$.
Then, divide the numerator by the denominator: $m=\frac{1210}{1.9404}\approx 623.6\ g$.

Answer:

$\approx 624\ g$ (or more precisely, approximately 623.6 g)