Energy and cost savings from turning down the thermostat?

[Sorbik]

I liked this problem because it's something you can use to talk about money savings w/ other people. Just making sure everything was done right though.

Homework Statement

the interior temperature of the room is typically 34.6°F (

the thermostat is typically set for 70.7°F.

you propose to lower the thermostat to 60.1°F.

Currently the building measures 23.5 × 34.5 × 14.5 feet

How much heat will be saved each morning by bringing the building up to the new operating temperature of 60.1°F instead of 70.7°F?

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.

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part 2:

electricity rate is $6.56 per kilowatt-hour. How much money (in dollars) is saved each morning by only heating the room to 60.1F?

Homework Equations

diatomic gas:

C_v = (5/2) R

R = 8.3144621 J/ mol*K

The Attempt at a Solution

edit: found out both of my answers were wrong.

 

[DrClaude]

Joules required to cause the temp change T is Q = m*Cv *ΔT where ΔT is change in Kelvin from 70.7°F to 60.1°F

Q = 396.5259 * 20.786 * 5.888 = 48,537.327 J

Advice: use units throughout to make sure everything is consistent.

 

[Sorbik]

Ok.

n=PV/RT

n= [(101,325)(332.889)] / [(8.3144)(294.65)] = 13,768.25 mol
both of these answers are wrong too. Not sure where I'm botching this

 

[DrClaude]

the interior temperature of the room is typically 34.6°F (1.444444C) (274.5944 K)


Assume that in the morning the pressure in the room is atmospheric. (1 atm = 101 325 pascals)

n=PV/RT

n= [(101,325)(332.889)] / [(8.3144)(294.65)] = 13,768.25 mol

You're not being consistent here. Number of moles should be calculated from the conditions in the morning.

There might be other errors (I haven't checked thoroughly), but you should fix this first.

 

[gneill]

Consider that as the temperature rises the air will want to expand. Presumably the building is not air tight and pressure should remain at 1 atm. This means the number of moles to be heated will decrease as temperature rises... I see an integration in your future

 

[DrClaude]

Consider that as the temperature rises the air will want to expand. Presumably the building is not air tight and pressure should remain at 1 atm. This means the number of moles to be heated will decrease as temperature rises... I see an integration in your future

Fortunately, no. The problem states: "Ignore heat and air losses to the outside."

 

[gneill]

Fortunately, no. The problem states: "Ignore heat and air losses to the outside."

Aurgh! I must've skimmed too lightly over that line; I only registered the heat loss bit. Thanks for catching that for me!

(Mind you, the integration would not be a difficult one)

 

[Sorbik]

great. It worked out using moles calculated from the temp K during morning time.