Mass/energy problem

[462chevelle]

Homework Statement

if you burn 1 gallon of gas and it makes 48kJ. can you calculate the amount of mass lost.

Homework Equations

law of conservation: Energy cannot be created or destroyed it just changes form.

The Attempt at a Solution

the way i look at this problem is that there is no loss of mass. the mass is just converted from a liquid to a gas since you cannot destroy energy. but i feel like i shouldnt be looking at it this way and i should be thinking of a way to model it in an equation. the question header is rest energy. and the only equation the book has under rest energy is e=mc^2. and i dont feel like that would apply here since i know all the variables. i dont need to solve for anything. any ideas?

thanks,
Lonnie

 

[phinds]

If there is no mass lost at all, where did the heat energy come from?

 

[462chevelle]

would the mass converted to heat energy be considered loss of mass?

 

[haruspex]

would the mass converted to heat energy be considered loss of mass?

If the heat is lost, yes. But if it is burnt within a closed system, so the heat stays there, I do not see why there should be s loss of mass.

 

[462chevelle]

hmm. so as vague as the question is I bet there are 2 answers. that there is no loss of mass if its a closed system and the amount of mass it would lose if it loses all the heat from the system.

 

[462chevelle]

so.
initial mass= 2.8kg
final mass = 48kJ=m(3x10^8)^2
final mass-initial mass=mass lost
does this look like the correct way to model this problem?
I think im still going to answer with 2 answers with a ya but,

thanks,
Lonnie

 

[haruspex]

so.
initial mass= 2.8kg
final mass = 48kJ=m(3x10^8)^2
final mass-initial mass=mass lost
does this look like the correct way to model this problem?
I think im steal going to answer with 2 answers with a ya but,

thanks,
Lonnie

No, you're ignoring the mass of the waste products. If the heat is lost then the mass lost is the mass equivalent of the heat energy.

 

[462chevelle]

so I just convert joules to kg and if I have 48000 joules. in kg that is 2.0833 X 10^-5??

 

[haruspex]

so I just convert joules to kg and if I have 48000 joules. in kg that is 2.0833 X 10^-5??

Yes.

 

[462chevelle]

thanks. that makes it a lot more clear. i am clearly overthinking this stuff.