Show that energy and mole balances yield the following differential equation:
The heating of a home to increase its temperature must be modeled as an open system because expansion of the household air at constant pressure results in leakage of air to the outdoors. Assuming that the molar properties of air leaving the home are the same as those of the air in the home.
Here, Q? is the rate of heat transfer to the air in the home, and t is time. Quantities P, V, n, and U refer to the air in the home.
What will be an ideal response?
Performing an energy and material balance on a home, the only sources of energy loss are from the air, enthalpy, and internal energy and the only material loss is the air. This gives:
By substituting, we obtain
and know that U = H–PV
We can obtain
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