Finding U-value for Wall with Plasterboard Lining and Air Gap

[bobred]

Homework Statement

There is a wall 100 mm thick, find the U-value. Then a plasterboard lining is added of thickness x and a gap between it and the wall of 20 mm

wall thickness b=0.1m, thermal conductivity \kappa_1=0.5 W m^{-1} K^{-1}
plasterboard thickness xm, thermal conductivity \kappa_2=0.1 W m^{-1} K^{-1}
Air gap g=0.02m,
Heat transfer coeff inside h_{in}=10 W m^{-2} K^{-1}
Heat transfer coeff outside h_{out}=100 W m^{-2} K^{-1}
Combined heat transfer coeff air gap h_{c}=10 W m^{-2} K^{-1}
Temp inside \Theta_1 = 300 K
Temp outside h_{c}= 270 K
Cross sectional area A

Homework Equations

For just the wall
rate of heat transfer q=\frac{UA(\Theta_1-\Theta_2)}{b} where
U=(\frac{1}{h_{in}}+\frac{b}{\kappa_1}+\frac{1}{h_{out}})^{-1}

For wall and plasterboard
rate of heat transfer q=\frac{UA(\Theta_1-\Theta_2)}{b} where
U=(\frac{1}{h_{in}}+\frac{b}{\kappa_1}+\frac{1}{h_{c}}+\frac{x}{\kappa_2}+\frac{1}{h_{out}})^{-1}

The Attempt at a Solution

I can work out the U-value for the wall, but I am asked then to find the U-value for the wall after lining, I can't see how to get this without having x.

Any ideas, Thanks

 

[bobred]

Mistake above
h_{c}= 270 K should read \Theta_{2}= 270 K and both q=\frac{UA(\Theta_1-\Theta_2)}{b} should be q=UA(\Theta_1-\Theta_2)

Any ideas?