Question

My husband and I always argue about the temperature in our house. I like it at 294.0 K, while he likes to set the thermostat to 300.0 degrees K. 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 50 kg of air. In the summer time, I pay about $0.14 per kWh of energy used. How much does it cost me every time we heat the air in the living room from 294.00 K to 300 K? (HINT: How many kWh does it take?) The heat capacity of our air is 1.01 J/(gC). 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.

Answer 1

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