As an accountant in charge of reducing expenditures for a lo

As an accountant in charge of reducing expenditures for a local company, you think you can save considerable money on fuel costs by lowering the room temperature of the building for daily use. In the morning, the interior temperature is typically 37.6degreeF and the thermostat is typically set for 71.4degreeF. Instead. you propose to lower the thermostat to 60.7degreeF. Currently the building measures 23.5 times 44.7 times 14.5 feet. How much heat will be saved each morning by bringing the building up to the new operating temperature ot bUVT instead of 71.4T? Ignore heat and air losses to the outside and consider air an ideal diatomic 9as- Assume that in the morning the pressure in the room is atmospheric. Express your answer as a positive quantity. The electricity rate in your area is $7.56 per kilowatt-hour. How much money (in dollars) is saved each morning by only heating the room to the new operating temperature?*

Solution

volume of the room = 23.5x44.7x14.5 ft

                                      = (23.5x44.7x14.5 )*(30.5)³ cc    ( 1ft = 30.5 cm)

                                       = 4.32e+5 dm³

molar volume of any ideal gas = 22.414 dm³ at STP

volume of the room in moles = 4.32e+5/22.414 = 1.93e+4 moles

change in temp = 71.4 -60.7 = 10.7⁰ F = 10.7*100/180 = 5.94⁰C

specific heat of air at constant pressure

       C_p = 29.1 J/mol-k, we use C_p as the pressure is constant

heat required to raise the temperature of the room by 10.7⁰ F or 5.94⁰ C or K

Q = 29.1*5.94*1.94e+4 J

        =3353.3676   KJ

no time is given hence we take

   1kw-hr as 1kJ of energy consumed

energy cost 7.56$ per kJ

energy cost saved = 3353.3676*7.56 = 25351 $