A chemical reaction takes place in a spherical pressure vessel. The rate of heat release per unit volume from the reaction in Btu/ft3 is q = K times eθ/1,000
where θ is the absolute temperature in the vessel in R. The internal diameter of the sphere is 2 ft, its wall, of thermal conductivity 10 Btu/ ft h R, is 6 inches thick and it is covered with a 2inch thickness of lagging of conductivity 1 Btu/ft h R.
If the heat transfer coefficient between the lagging and the atmosphere, which is at 60 F, is 3 Btu/ ft2 h R and the temperature in the vessel at which the reaction proceeds in equalibrium is 740F,
Determine the value of the constant K, in the reaction equation. Derive from first principles any equation used.