Question

A house is maintained at 1 atm and 24°C, and warm air inside a house is forced to leave the house at a rate of 90 m3/h as a result of outdoor air at 5.5°C infiltrating into the house through the cracks. Determine the rate of net energy loss of the house due to mass transfer. The gas constant of air is R

Answer 1

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Specific heat of air at constant pressure = 1.005KJ/kg-K Apparently the hot air leaves the house while equal quantity of the cool air passes inside (Neglecting the small specific volume changes between the hot and the cold air) So the situation can be sampled as a scenario where there is continuous draw down of the thermal energy from the air.

Answer 2

We have that for the Question,it can be said that  the rate of net energy loss of the house due to mass transfer

$E=0.567kW$

From the question we are told

A house is maintained at 1 atm and 24°C, and warm air inside a house is forced to leave the house at a rate of 90 m3/h as a result of outdoor air at 5.5°C infiltrating into the house through the cracks.

Generally the equation for the density  is mathematically given as

$\rho=\frac{P}{RT}\\\\Therefore \\\\\rho=\frac{101.325}{0.287*297}$

$\rho=1.189kg/m^3$

Generally the equation for the mass flow rate  is mathematically given as

$m=\rho v\\\\m=1.189*90\\\\m=107.01kg/h$

$m=0.029725kg/s$

Therefore

Energy loss

$E=Eout-Ein\\\\E=mCp*(T2-T1)\\\\E=0.029725*1.005*(24-5)$

$E=0.567kW$

Therefore

the rate of net energy loss of the house due to mass transfer

$E=0.567kW$

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