Final temperature of the water after adding heat?

[lavendly]

Homework Statement

You add 1500 cal of heat to a cup of water at 22.5ºC. The water has a mass of 500.0g. What is the final temperature of the water?

Homework Equations

Q=mcΔT

The Attempt at a Solution

so i tried solving it by finding the energy of the water
Q=(500g)(1.0cal/g)(22.5ºC)
Q=11250 cals

then i tried adding 11250 cals to the 1500 cals that was added onto it from the problem and got 12750 cals.

using 12750 cals as Q, i set up Q=mcΔT and plugged in all the known variables and solved for change in T, which was 25.5ºC. I took this change in T and added it to the initial temperature of 22.5ºC, and got 48ºC for the final temperature of the water. Is that right? I didn't get an answer sheet and I have a test tomorrow so I have no idea if I'm doing this right or not

 

[Orodruin]

It is not $\Delta T$ that is 22.5 °C - it is the initial temperature. You are asked to find the final temperature. What you are computing would be the heat required to heat the water by 22.5 °C from where it was initially.

 

[epenguin]

A calorie is the amount of heat needed to increase the temperature of 1g of water by 1 degree, the problem is only to know the definition and simple arithmetic.