# A sample of mercury absorbed 257 J of heat and its mass was .45 kg. If it's temperature increased by 4.09 K, what is its specific heat in J° / kg K?

Jan 18, 2017

The specific heat formula is:

c = Q/(m × ΔT)

Where:

$c$: specific heat, in J/(kg.K)

$Q$: heat required for the temperature change, in J

ΔT: temperature change, in K

$m$: mass of the object, in kg

For our equation, we are given everything in the right units, so all we need is to plug in the numbers.

c = Q/(m × ΔT)

$c = \frac{257}{.45 \times 4.09}$

$c = 139.64 \frac{J}{k g \times K}$

Jan 18, 2017

The specific heat of mercury to two significant figures is "140 J"/("kg"*"K").

#### Explanation:

Use the equation $\textcolor{red}{Q = m c \Delta t}$, where $Q$ is energy gained or lost in Joules; $m$ is mass, in this case kg; $c$ is specific heat, in this case in $\text{J"/("kg"*"K")}$; and $\Delta t$ is change in temperature, in this case Kelvins.
Determine what variables are known, and unknown. Then solve the equation for the unknown variable.

Known
$Q = \text{257 K}$
$m = \text{0.45 kg}$
$\Delta t = \text{4.09 K}$

Unknown
${c}_{\text{Hg}}$

Solution
Rearrange the equation to isolate ${c}_{\text{Hg}}$. Substitute the known values into the equation and solve.

c_"Hg"=(Q)/(m*Deltat)=(257"J")/((0.45"kg")xx(4.09"K"))="140 J"/("kg"*"K") rounded to two signficant figures