Question

How much heat is needed to raise the temperature of 5.28 gallon of water from 25degreeaC to 88 degreesC ? (1gal=3.785L ; 1L = 1000mL ; density of water is 1.00g / 1.00mL ; the specific heat of water is 4.184 J/g/degreesC)

Answer 1

The first step to answer this question is to convert the given gallons to liters and then to mililites using the given conversion factors:

`5.28gal\cdot(3.785L)/(1gal)\cdot(1000mL)/(1L)=19984.8mL`

The second step is to convert the volume of water to mass using its given density:

`19984.8mL\cdot(1.00g)/(mL)=19984.8g`

Finally, use the following formula to find the heat needed to raise the temperature of water:

`Q=Cp\cdot m\cdot\Delta T`

Where Q is the heat, Cp is the specific heat, m is the mass and ΔT is the difference of temperatures. Replace for the given values and find Q:

`\begin{gathered} Q=4.184J/g\degree C\cdot19984.8g\cdot(88\degree C-25\degree C) \\ Q=5,267,833.4J \end{gathered}`

It means that the heat needed to raise the temperature of water is 5267833.4J.