# How much heat is required to warm a 215 g cup of water from 21 degree C to 85 degree C?

## Question:

How much heat is required to warm a {eq}215 \ g {/eq} cup of water from {eq}21^\circ \ C {/eq} to {eq}85^\circ \ C {/eq} ?

## Heat Transfer Equation:

The heat transfer equation is known as {eq}\displaystyle q = mc\Delta T {/eq}. Here, we relate the transferred heat, q, to a certain sample with a mass, m, specific heat, c, and its corresponding change in temperature, {eq}\displaystyle \Delta {/eq}T, wherein no chemical reaction or phase transformation takes place.

Determine the heat required, q, in order to increase the temperature of the given amount of water using the equation, {eq}\displaystyle q = mc\Delta T {/eq}, where m = 215 g is the mass of the water and {eq}\displaystyle \Delta {/eq}T = 85{eq}\displaystyle ^\circ {/eq}C - 21{eq}\displaystyle ^\circ {/eq}C = 64{eq}\displaystyle ^\circ {/eq}C is the change in temperature we want to attain. We must know that the specific heat of water is c = 1 cal/g{eq}\displaystyle ^\circ C {/eq}. We proceed with the solution.

{eq}\begin{align} \displaystyle q &= mc\Delta T\\ &= 215\ g\times 1\ cal/g^\circ C\times 64^\circ C\\ &\approx\boxed{\rm 13760\ cal} \end{align} {/eq}