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paque
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A homeowner finds that, if she turns down her thermostat by 3[degrees C] she can reduce the rate at which heat is lost to outside, by 10%. If the outside temperature is -5[degrees C], what are the Thermostat readings before and after the adjustment.
I'd just like verification that i haven't screwed up this problem totally...
[because I'm just sort of going along blindly, moving on when I touch something...]
My teacher gave me this equation:
d Q/ d t{ime} = (T{emp hot} - T{emp cold}) * A{surface area} * K(conductivity constant) / L{ength of conducted material}
dQ/dt = (T(h) - T(c)) * A * K / L
While i know this equation:
Q = mc/\T
However, i chose to use sole my teacher-given equation...
dQ/dt = (T(h) - T(c)) * A * K / L
and instead equated it to
/\Q//\t = (T(h) - T(c)) * A * K / L
(i used change in heat/time, I'm not so good with calculus :tongue: )
/\Q//\t = (T(h) - T(c)) * A * K / L
I decided that the orange terms would be kept constant.
Constant = (T(h) - T(c)) / (/\Q)
then i chose two thermostat readings to be equal to that constant
(Before thermostat change) Constant = (To - (-5) / (Q)
(After thermostat change) Constant = ((To - 3) - (-5) / (.9Q)
I then set the two equations equal to each other, via the constants, canceled out the Q on both sides, Solved for To,
and got
75[degrees C] for the beginning Temperature...
Any suggestions?
I'd just like verification that i haven't screwed up this problem totally...
[because I'm just sort of going along blindly, moving on when I touch something...]
My teacher gave me this equation:
d Q/ d t{ime} = (T{emp hot} - T{emp cold}) * A{surface area} * K(conductivity constant) / L{ength of conducted material}
dQ/dt = (T(h) - T(c)) * A * K / L
While i know this equation:
Q = mc/\T
However, i chose to use sole my teacher-given equation...
dQ/dt = (T(h) - T(c)) * A * K / L
and instead equated it to
/\Q//\t = (T(h) - T(c)) * A * K / L
(i used change in heat/time, I'm not so good with calculus :tongue: )
/\Q//\t = (T(h) - T(c)) * A * K / L
I decided that the orange terms would be kept constant.
Constant = (T(h) - T(c)) / (/\Q)
then i chose two thermostat readings to be equal to that constant
(Before thermostat change) Constant = (To - (-5) / (Q)
(After thermostat change) Constant = ((To - 3) - (-5) / (.9Q)
I then set the two equations equal to each other, via the constants, canceled out the Q on both sides, Solved for To,
and got
75[degrees C] for the beginning Temperature...
Any suggestions?