# What’s the final temperature in Kelvin of 1.5 gallons of water, with an initial temperature of 50 Fahrenheit, if you add 432 kJ to the water?

Feb 26, 2018

301 K

#### Explanation:

I converted into standard units for the solutions. (I approximated gallons and assumed you meant US gallons)
5.68 litres= 1 US gallon
50 Fahrenheit=10 Celcius= 283 Kelvin, our starting temperature.

Using the equation:
$Q = m c \Delta T$
Where $Q$ is the energy put into a substance in joules (or kilojoules),
$m$ is the mass of the substance in kilograms.
$c$ is the specific heat capacity of the substance you put the energy into. For water it is 4.187 kj/kgK (kilojoule per kilogram per kelvin)
$\Delta T$ is the temperature change in Kelvin (Or celsius as 1 step up or down on the Celcius scale is equivalent to that of the Kelvin scale).

Now, water can be assumed to weigh 1 kg per liter, thus 5.68 litres=5.68 kg of water.

Hence:

$432 = \left(5.68\right) \times \left(4.187\right) \times \Delta T$

$\Delta T \approx 18 K$
So we increased or temperature by 18 degrees Kelvin, hence our final temperature is:

$283 + 18 = 301 K$