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The Rate of change in temperature of gas. An object of mass "m" specific heat "Cp" and surface area "As" and initially at a temperature "T0".

The differential equation involving rate of increase of object temperature T with respect to time t is given by:

mCpdT/dt = hA(Tg-T) where the meaning of the symbols have been given in the problem

Solving the differential equation:

mCpdT/dt +hAT= hAT
dT/dt + hAT/mCp = hATg/mCp
This diff equation can be solved by integrating factor.

I.F. = e^( ∫hAdt/mCp) = e^(hAt/mCp)

The differential equation becomes:

Te^(hAt/mCp) = (hA/mCp)( ∫(Tge^(hAt/mCp))dt)

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