# Math Help - Joint And Inverse Variation

1. ## Joint And Inverse Variation

The heat lost through a windowpane varies jointly as the difference of the inside and outside temperatures and the window area, and inversely as the thickness of the pane. In one hour, 49.5 joules of heat are lost through a pane 40 cm by 28 cm that is 0.8 cm thick, when the temperature difference is 44 degrees celsius. How many joules are lost in one hour through a pane 0.5 cm thick having an area that is 0.25 times the area of the other pane, when the temperature difference is 40 degrees celcius.

2. Originally Posted by sp0rtskid55

The heat lost through a windowpane varies jointly as the difference of the inside and outside temperatures and the window area, and inversely as the thickness of the pane. In one hour, 49.5 joules of heat are lost through a pane 40 cm by 28 cm that is 0.8 cm thick, when the temperature difference is 44 degrees celsius. How many joules are lost in one hour through a pane 0.5 cm thick having an area that is 0.25 times the area of the other pane, when the temperature difference is 40 degrees celcius.

Let D be the temp difference, A be the area, and P be the thickness of the pane.

If E is the Energy lost then

$E=k\left( \frac{DA}{P}\right)$

$49.5=k\left( \frac{(44)(40)(28)}{0.8}\right)$

Solving this equation for k gives

$k=\frac{9}{11200}$

$E=\frac{9}{11200}\left( \frac{DA}{P}\right)$

Now we just use the values given above

$E=\frac{9}{11200}\left( \frac{(40)(.25)(40)(28)}{0.5}\right)=18$

I hope this helps

Good luck.