With reference to Prob. 2.47, assume air to be an ideal gas, and develop an expression giving the household air temperature as a function of time.

Problem 2.47

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, show that energy and mole balances yield the following differential equation:

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.

Transcribed Image Text:

dn +n- dt dU Q =-PV- dt