# If the specific heat of mercury is 0.14 J/g°C, how much heat is required to raise the temperature of 250.0g of mercury from 10°C to 62°C?

Oct 31, 2015

$\text{1.8 kJ}$

#### Explanation:

A substance's specific heat tells you how much heat is required to increase the mass of $\text{1 g}$ of that substance by ${1}^{\circ} \text{C}$.

The equation that establishes a rel;ationship between heat absorbed and change in temperature looks like this

$\textcolor{b l u e}{q = m \cdot c \cdot \Delta T} \text{ }$, where

$q$ - heat absorbed
$m$ - the mass of the sample
$c$ - the specific heat of the substance
$\Delta T$ - the change in temperature, defined as the difference between the final temperature and the initial temperature of the sample

You have all the information needed to find the amount of heat required to increase the temperature of your sample of mercury by that many degrees Celsius, so just rearange the above equation and solve for $q$

q = 250.0color(red)(cancel(color(black)("g"))) * 0.14"J"/(color(red)(cancel(color(black)("g"))) color(red)(cancel(color(black)(""^@"C")))) * (62 - 10)color(red)(cancel(color(black)(""^@"C"))) = "1820 J"

I'll leave the answer rounded to two sig figs and expressed in kilojoules

$q = \textcolor{g r e e n}{\text{1.8 kJ}}$