# Insulating a cat house

1. May 2, 2014

### TheKShaugh

Hi,

I'm trying to build a cat house and I thought I would calculate the exact thickness of insulating material I would need in order to keep my cat toasty when it gets cold. I'm not sure if I have the right process though. I thought I would ball park how many calories a cat burns in an hour using internet data, convert to watts, and then use the heat flow rate equation: $$W = \frac{k_h A \Delta T}{x}$$ where W is less power than the cat outputs, A is the area of the box, delta t is the difference between average outside temperature and the temperature of the cat, k is the thermal conductivity constant of the material, and x is the required thickness. One issue I see is that the temperature in the box will rise at a linear/exponential (?) rate rather than be constant, but I'm not sure how to factor that in as I've never done calculus based physics, so is using the temperature of the cat for delta T going to lead to a decent approximation?

Does anyone have any tips for how I can find this information?

Thanks!

2. May 2, 2014

### 256bits

I would use the lowest outside temperature instead of the average.

3. May 3, 2014

### SteamKing

Staff Emeritus
Dang, I always just provided a box the cat could get in and out of. I thought he could figure out the rest about staying warm. If the cat didn't take calculus based physics at school, that was his problem.

BTW, for those not familiar with the American idiom, 'cat house' usually refers to a place where no cats actually live, but plenty of other, ahem, activities occur after suitable price negotiations have concluded.

4. May 5, 2014

### voko

I second SteamKing's suggestion: leave figuring out how to keep warm to the cat, they are good at that.

Purely as an exercise in physics, though, it might be easier to consider a steady (equilibrium) situation, where the temperature in the box is constant and the power generated by the cat is matched by the power leaking through the walls.