A cylinder and piston assembly (defined as the system) is warmed by an external flame. The contents of the cylinder expand, doing work on the surroundings by pushing the piston outward against the external pressure. If the system absorbs 559 J of heat and does 488 J of work during the expansion, what is the value of ΔE?

dE = q + w

dE = 559J + (-488) = ? J

Well, let me calculate that for you, but first let's acknowledge the pun in your question: the cylinder is being warmed by an external flame, so you could say it's getting "fired up"! Now, let's get to the math.

The first law of thermodynamics states that the change in internal energy (ΔE) of a system is equal to the heat absorbed (Q) minus the work done (W) by the system. So, in this case:

ΔE = Q - W

Substituting the values given:

ΔE = 559 J - 488 J

ΔE = 71 J

So, the change in internal energy (ΔE) of the system is 71 J. It seems like the system got a little "heated" during this process!

The value of ΔE (change in internal energy) can be determined using the First Law of Thermodynamics, which states that the change in internal energy of a system is equal to the heat absorbed by the system minus the work done by the system on the surroundings. Mathematically, it can be represented as:

ΔE = Q - W

Where:
ΔE = Change in internal energy
Q = Heat absorbed by the system
W = Work done by the system

Given that the system absorbs 559 J of heat (Q = 559 J) and does 488 J of work (W = 488 J), we can substitute these values into the equation:

ΔE = 559 J - 488 J

Now, we can calculate the value of ΔE:

ΔE = 71 J

Therefore, the change in internal energy (ΔE) is 71 J.

To find the value of ΔE (the change in internal energy) of the system, we can use the First Law of Thermodynamics, which states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system.

Mathematically, ΔE = Q - W

Where:
ΔE = change in internal energy
Q = heat added to the system
W = work done by the system

Given:
Q = 559 J (heat absorbed by the system)
W = 488 J (work done by the system)

Using the values given, we can substitute them into the equation:

ΔE = 559 J - 488 J

Now, we can calculate the value of ΔE:

ΔE = 71 J

Therefore, the change in internal energy (ΔE) of the system is 71 J.