Question

A slab of cross sectional area A and thickness L has a thermal conductivity k. When a temperature difference ΔT is applied across the ends of the slab, a heat flow rate H is observed.

Answer 1

Complete each of the statements below, using the following choices

A.stays the same
B.doubles
C.quadruples
D.decreases by a factor of 2
E.decreases by a factor of 4
F.changes by a factor other than ¼, ½, 1, 2, or 4

i.If A increases by a factor of √2, H _______.
ii.If L increases by a factor of 2 and ΔT increases by a factor of 2, then H _______.
iii.If k increases by a factor of 2, the R factor _______.
iv.If ΔT increases by a factor of 2, then H _______.
v.If L increases by a factor of 2, then H _______.
vi.If A decreases by a factor of 2, then H _______.

Now I've selected i.(change by a factor other than 1/4 etc.)
ii. Stay the same
iii. double
iv. double
v. decrease by factor of 2
vi.doubles
could someone help me to figure out where I went wrong and why?

Answer 2

@ybarrap if you can get the chance to take a peak at this it would be appreciated

Answer 3

Are you using this equation for the general case
$$
HL= A\int_{T_L}^{T_H} k(T) \mathrm{d}T
$$
or
$$
H= kA\frac{T_H-T_L}{L}
$$
for small temperature differences?

Either way, based on these equations, I get the same answers you did!

I used this as a reference - http://en.wikipedia.org/wiki/Thermal_conductivity#Equations

Answer 4

The problem with my answers were iii and iv which ended up being decreased not double. Due to me reading the questions wrong at first thank you for taking a look. @ybarrap