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 of 60.7degreeF instead of 71.4degreeF? Ignore heat and air losses to the outside and consider air an ideal diatomic gas. 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?* * This represents only a fraction of the cost savings, since higher intenor temperatures induce higher losses of heat to the outside.

Solution

Part 1

Total internal energy saved from lowering of the temperature from 71.4F to 60.7F = (f/2)nRT

Since air is diatomic f=5, n=number of moles of air, R=8.31 J/mol.k,

71.4F = 21.8888°C & 60.7F = 15.944°C

T= (21.888°C -15.944°C)=5.94°C=5.94K

Volume = 23.5x44.7x14.5 ft³ = 7.16x13.62x4.42 m³=431 m³

Total air mass in the building = Volume x air density = 431 m³ x 1.225 kg/m³ = 528Kg

Air molecular weight = 28.97 g/mol.

Number of moles = 528/(28.97/1000) = 18226 moles

Total energy saved = (5/2)x18226x8.31x5.94=2249KJ = 2249000J

Part 2

Electricity rate = $7.56 per kilowatt-hour= ($7.56/1000x60)per Watt.Second = ($7.56/1000x60) per Joule

Total money saved = 2249000x($7.56/1000x60)= $283.4