# How many joules are required to heat 15.2 g of water at 35.0°C to 70.0°C?

Dec 14, 2015

$\text{2,220 J}$

#### Explanation:

In order to be able to determine how much heat is required to increase the temperature of your sample of water from ${35.0}^{\circ} \text{C}$ to ${70.0}^{\circ} \text{C}$, you need to know the value of water's specific heat.

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

Water has a specific heat of about 4.18 "J"/("g" ""^@"C"). This tells you that in order to increase the temperature of $\text{1 g}$ of water by ${1}^{\circ} \text{C}$, you need to provide it with $\text{4.18 J}$ of heat.

Now, here's how you can think about what's going on here. in order to increase the temperature of $\text{4.18 g}$ of water by ${1}^{\circ} \text{C}$, you would need $4.18$ times more heat than water's specific heat value.

Likewise, in order to increase the temperature of $\text{4.18 g}$ of water by ${4.18}^{\circ} \text{C}$, you'd need $\left(4.18 \times 4.18\right)$ times more heat than water's specific heat value.

In your case, you need to increase the temperature of $\text{15.2 g}$ of water by ${35.0}^{\circ} \text{C}$, which tells you that you're going to need $\left(15.2 \times 35\right)$ times more heat than water's specific heat value.

Mathematically, this is expressed as

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

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

Plug in your values to get

$q = 15.2 \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{g"))) * 4.18"J"/(color(red)(cancel(color(black)("g"))) color(red)(cancel(color(black)(""^@"C")))) * (70.0 - 35.0)color(red)(cancel(color(black)(""^@"C}}}}$

$q = \text{2223.76 J}$

Rounded to three sig figs, the answer will be

$q = \textcolor{g r e e n}{\text{2,220 J}}$