# How much energy (in joules) is required to raise the temperature of 200g of liquid water from 20c to 50 c?

## Heat Capacity of liquid water: 4.2 J/(g*K) Latent Heat of fusion of water: 330 J/g Latent heat of vaporization of water: 2200 J/g

Feb 11, 2018

$25200 J$

#### Explanation:

$E = m c \Delta \theta$

where $c$ is specific heat capacity in $J / g / K$

(specific heat capacity: the amount of energy needed to raise the temperature of $1 g$ of a substance by $1 K$)

and $\Delta \theta$ is the change in temperature.

here, $\Delta \theta = {50}^{\circ} C - {20}^{\circ} C = {30}^{\circ} C$.

$E = 200 g \cdot 4.2 J / g / K \cdot 30 K$

$= 25200 J$

Feb 12, 2018

It's about 25 kJ - make sure you're consistent in your units.

#### Explanation:

The calculation is $E = M . c . \theta$

Where $E$ is the energy in J, $M$ is the mass of substance in g, $c$ is the specific heat (of water in this case) in $\frac{J}{g . K}$, and $\theta$ is the temperature change (which can be in celcius or kelvin - if you're only looking at the delta between the two temperatures it makes no odds which unit you choose).

So it works out like this

$E = M . c . \theta$
$E = 200 \times 4.2 \times 30$

So E= 25,200 J (or 25.2 kJ).