Energy Balance Around Tank

The next step is to write an energy balance around the tank. Here we neglect the kinetic and potential energy changes between the inlet and outlet streams and the shaft work done by the mixing impeller:

accumulation = in by flow + in by heat transfer - out by flow

and using the assumptions of constant density, volume and heat capacity, we find

or

but

is a constant, so

and

We must also perform a material and energy balance around the jacket and use the connecting relationship for heat transfer between the jacket and the tank.