# What happens to the heat of water if the temperature is cooled from 25.0 degrees Celsius to 10.0...

## Question:

What happens to the heat of water if the temperature is cooled from 25.0°Celsius to 10.0°Celsius if you have 10.0 g of water?

## Heat Transfer:

The heat transferred to a given system can be determined from a change in the system's temperature. For a given sample of a substance with a mass m and a specific heat c, we relate the heat transferred q to the change in temperature, {eq}\displaystyle \Delta {/eq}T, using the equation:

{eq}\displaystyle q = mc\Delta T{/eq}

We will determine the heat exchanged, q, in the given system using the equation:

{eq}\displaystyle q = mc\Delta T{/eq}, where:

• {eq}\displaystyle m = 10.0\ g{/eq} is the mass
• {eq}\displaystyle c = 1\ cal/g ^\circ C{/eq} is the specific heat
• {eq}\displaystyle \Delta T = 10.0 ^\circ C - 25.0 ^\circ C = -15.0 ^\circ C{/eq} is the temperature change of the sample

We proceed with the solution:

{eq}\begin{align} \displaystyle q&= mc\Delta T\\ &= 10.0\ g\times 1\ cal/g ^\circ C\times -15.0 ^\circ C\\ &= -150.\ cal \end{align}{/eq}

The heat of the water is decreased by -150 cal due to cooling.