Appropriate units for temp problem

[thebigskysky]

Homework Statement

(T-T envir)/(T int - T envir) = exp (-(2h/pcL)t)

T = temp (°C)
h = heat transfer
p = density (kg/m^3)
c = specific heat (J/Kg * K)
L = plate thickness (m)
t = Time (s)

What are the appropriate units for h? Show all steps... (equation is homogenous in units)

The Attempt at a Solution

(°C-°C) / (°C-°C) = exp(-(h/(Kg/m*m*m)(J/Kg*K)(m)) s
temp/temp = 1
(kg/m*m*m)(J/kg*K)(m) = exp (-h * s)
(m*m*J*K) = exp (-h * s)
(m^2)(JK) / s = -h
- (m^2)(JK) / s = h ?

heat transfer = negative meters squared time joules time kelvin all over seconds ?
seems a little weird to me... what did i do wrong... ty guys

 

[M Quack]

Positive or negative does not matter, it is the same units. If the temperature outside is -10 deg C or +35 deg C, it is still given in deg C.

The third line of your solition does not make sense. Why the exp on the right hand side?

The argument of the exponential has to be unitless.

[-(2h/pcL)t] = 1

[h] = [pcL/t] = ...

The result certainly looks odd. You can still write J as combination of other units, but that changes little.