A backpacker wants to carry enough fuel to heat 2.5 kg of water from 25 °C to 100.0 °C. If the fuel she carries produces 36 kJ of heat per gram when it burns, how much fuel should she carry? (For the sake of simplicity, assume that the transfer of heat is 100% efficient.)

Solution 103P :

Given :

Mass of water = 2.5 kg.

Ti = 25 °C

Tf = 100 °C

fuel she carries produces 36 kJ of heat per gram when it burns,

Mass of fuel she should carry = ?

Specific heat of water = 4.186 J/g °C

Step 1:

First let’s calculate :

= Tf - Ti [Tf -is the final temperature and Ti is the initial temperature]

= 100 - 25 = 75 °C

Now that we have all the data required , let’s calculate the heat energy required :

Q = mc

Q = 2.5 kg4.186 J/g °C75 °C

= 784.875 kJ