*Thanks for your response! Its 100 C. I did finally get to the answer, except I dont quite see how it links to the energy or entropy balances... Might you have an incling into how they could be linked?*

You original equation is a first law energy balance steady flow equation. Say you have a control volume such as a tank of liquid or whatever. So on the left side you have the change in energy per unit time of the energy contained inside of the tank =

= Change in energy per unit time = dU/dt inside the tank (control volume)

The change in energy per unit time in the control volume is equal to the engergy per unit time added to the volume minus the energy removed per unit time. This is equal to:

Heat (added or removed) per unit time = Qdot plus+

Work (added or removed) per unit time = Wdot plus+

Mass in minus mass out per unit time x the energy contained in that mass = Sum Mdot x (enthalpy/unit mass+KE per unit mass+PE per unit mass) for both in and out flow streams.

So your equation is one of a balance of energy based on the first law of thermodynamics.

But you don't have a flowing system. Your control volume is the piece or iron itself with no mass flowing in or out. I guess you could make it a flowing system say if you start with a 3kg piece of iron in a container then flow some molted iron in and out over a period of time and keep track of how much energy flows in versus out to find the net energy in or out of the system, but you don't have a flowing system - your system is the 3 kg of iron.

Therefore the terms involving mass in and mass out go away.

Now since you have a solid piece of iron that cannot change in volume you cannot have any work into or out of the system unless you drag the iron on the ground and cause frictional work to add energy to the iron in the form of heat but you don't have any movement of the iron either - so there is no work in or out of the system.

So that leaves you with the equation:

dU/dt = Qdot

Qdot is the heat added or removed from the system which in this case there is a net heat added of:

Qdot = (500 - 15) watts

So this is the increase in the internal energy of the system dU/dt

For any solid or liquid the increase in internal energy is (m)(Cp)(dT) since again there are no moving boundaries in the solid or liquid then all energy input as heat goes in to iincreasing the interal energy (increasing molecular vibrational/kinetic energy) since there is no moving boundaries like when you add heat energy to a gas where some of the energy may go into internal energy (kinetic energy of molecules - temperature) and some may go into moving boundaries (such as piston work). In the case of solid or liquid all heat added goes into kinietic/vibrational energy of molecules.

So the resulting equation is:

dU/dt=Qdot

= (Mdot)(Cp)(dT)/dt = 485 Watts.

Just like you solved in you last post above.

So the first law says that energy cannot be created or destroyed. All the energy in the universe already exist someplace and in some form in the universe. It can only be converted from one form into the other. So you are like an accountant just keeping track of where all of it goes.

**Edited by snickster, 11 September 2023 - 08:59 PM.**