# Homework Help: Heat and internal energy

1. May 6, 2015

### Monsterboy

1. The problem statement, all variables and given/known data
A perfectly insulated and sealed spherical vessel contains an air-fuel mixture,somehow the mixture is made to burn causing a rise in temperature of the vessel and it's contents.
2. Relevant equations
Then which of the following is correct?
A) Q=0 ,W=0 ,u=0
B)Q +ve ,W=0 ,u=+ve
C) Q=0 ,W=0 , u +ve

Q-amount of heat input to the system
W-work done by the system
u- change in internal energy.

3. The attempt at a solution

I feel the solution is B .As the chemical energy is converted to heat energy ,amount of heat energy is increased within the system. As the increase in heat energy leads to more energy for molecular motion it leads to an increase in internal energy.

The answer that was given to me was C , can we claim that Q=0 is correct ? just because the heat generated due to the ignition of the air-fuel mixture is inside a perfectly insulted and sealed container does that mean there is no increase in heat energy within the system ?

I know that change in total energy inside the system is zero because it is perfectly insulated and sealed, but that does that mean change in heat energy is zero ? ( we know that chemical energy converted to heat energy)

2. May 6, 2015

### Svein

Yes. There is no energy interchange with the environment since you have a "perfectly insulated and sealed spherical vessel".

3. May 6, 2015

### Staff: Mentor

Actually, answer C is incorrect (with all due respect to whomever gave you that as the answer). Svein has already pointed out that Q is zero, since Q represents the heat transferred from the surroundings to the system. And W is zero, since the walls of your system are rigid. So, from the first law of thermodynamics, ΔU = 0. So, C can't be correct because it violates the first law of thermodynamics.

The correct answer is A. In a system where chemical reaction takes place, the internal energy is a function not only of temperature and volume, but also a function of the number of moles of each species that is present. And, since, with a chemical reaction, the number of moles of the various species in the final state of the system is different from the initial state, the temperature has to change to offset the difference between the internal energies of the product species and the internal energies of the reactant species (in a way such that the overall internal energy remains constant).

Chet

Last edited: May 6, 2015
4. May 6, 2015

Thanks.

5. May 7, 2015

### Monsterboy

Internal energy is a function of volume? How?

6. May 7, 2015

### Staff: Mentor

The real question is, how not? You are aware that internal energy of a material is a point function of state, correct? So how many intensive physical properties of a gas or liquid (of constant composition) do you need to specify in order to establish its thermodynamic state (and thus its internal energy)? (Here are some intensive physical properties for you to consider: temperature, pressure, specific volume.)

You are thinking of an ideal gas, where the internal energy is a function only of temperature, right? That's because, for a real gas in the ideal gas limit (low pressures), the molecules are too far apart to interact with each other energetically. However, as you decrease the specific volume, the molecules get closer together, and the potential energy interactions between the molecules begins to contribute to its internal energy.

Chet

7. May 7, 2015

### Monsterboy

Yes , I seemed have developed a habit of assuming the gas to be ideal when I shouldn't.