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Boobers87 Boobers87
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Posts: 21
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8 years ago
My husband and I always argue about the temperature in our house. I like it at 76.0°F, while he likes to set the thermostat to 73.0°F. As we take turns constantly changing the setting, our poor heating and cooling system tries to keep up. I argue that it causes us to waste money. My living room contains 57 kg of air. In the summer time, I pay about $0.15 per kWh of energy used. How much does it cost me every time we heat the air in the living room from 73.0°F to 76.0°F? (HINT: How many kWh does it take?) The heat capacity of our air is 1.01 J/(g°C).
All work must be shown, labeled, and explained in detail to receive credit. Note that where applicable, superscripts (X2) can be written as X^2 and subscripts (X2) can be written as X_2 if it saves you time.
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wrote...
Educator
6 years ago
All you have to do is calculate the Heat with the following expression:
Q = m*cp*(Tf-Ti)

The temperature is in KElvin, let's convert that to ºC:
T1 = 294 - 273 = 21 ºC
T2 = 300 - 273 = 27 ºC

Now, let's calculate Heat for this range of temperature:
Q = 50000 * 1.01 * (27-21)
Q = 303000 J

Now 1 J = 1 Ws; so this value of Q is the same as Ws, so, let's convert this to kWh:
P = 303000 * (1/1000) = 303 kWs * 1h/3600s = 0.0842 kWh

So, the cost would be:
$ = 0.0842 kWh * 0.14 $/kWh = 0.0118 $

Hope this helps
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