# How much energy does it take to heat 10 mL up 30 degrees Celcius in kilocalories?

## Question:

How much energy does it take to heat 10 mL up 30 degrees Celcius in kilocalories?

## Heat Transfer:

The heat transferred to a substance will correspond to a change in temperature. We determine the total heat transferred to the substance by measuring the mass, {eq}\displaystyle m {/eq}, and the change in temperature, {eq}\displaystyle \Delta T {/eq}, and then applying the equation, {eq}\displaystyle q = mc\Delta T {/eq}, where {eq}\displaystyle c {/eq} is the specific heat capacity of the substance. We can acquire {eq}\displaystyle c {/eq} by searcing for standard values or by calorimetry experiments.

## Answer and Explanation:

Determine the energy required, {eq}\displaystyle q {/eq}, to raise the temperature of {eq}\displaystyle 10 mL {/eq} of water by {eq}\displaystyle \Delta T = 30 ^\circ C {/eq}, using the equation, {eq}\displaystyle q=mc\Delta T {/eq}, where the specific heat of water is {eq}\displaystyle c= 1\ cal/g ^\circ C {/eq}. Assuming a density of {eq}\displaystyle 1\ g/mL {/eq}, we determine the mass of the water as {eq}\displaystyle 10\ mL\times 1\ g/mL = 10\ g {/eq}. We proceed with the solution.

{eq}\begin{align} \displaystyle q &= mc\Delta T\\ &= 10\ g\times 1\ cal/g ^\circ C\times 30 ^\circ C\\ &= 300\ cal\\ &= 0.3\ kcal \end{align} {/eq}