The heat input to a cold box is to be reduced by adding extruded polystyrene sheets ( p=55kg m^-3 , k=0.027W m^-1 K^-1 , Cp=1.21kJ kg^-1 K^-1) to all sides. The box is 3 feet on a side and all sides are in contact with air. when the box is placed in a constant-temperature room which is maintained at 70 degrees F, the heat loss is 40,000 Btu h^-1. It is desired to redue this by a factor of 100 while maintaining the inside temperature at -30 degrees F. find the appropriate insulation thickness in inches.