Process Energy Balance

Signs of heat and work

The first law states that energy is conserved. For a closed system, subtract work delivered by the system from heat supplied to it to find the total energy change. If 100 kJ of heat enters while the system delivers 30 kJ of work, its energy increases by 70 kJ. Enter work supplied to the system as a negative value. An adiabatic compression then gives a positive energy increase.

Steady flow

For a device with one inlet, one outlet and no accumulation, heat duty equals the enthalpy increase rate plus shaft power delivered. A flow of 2 kg/s with enthalpy rising from 100 to 150 kJ/kg and 20 kW of work output requires 120 kW of heat. Both enthalpies must share the same reference. The calculation excludes changes in velocity or elevation, chemical reactions and any model of heat losses from the equipment.

Read the negative sign in a cooling duty

For a steady flow example, let mass flow be 1.5 kg/s, inlet enthalpy 240 kJ/kg and outlet enthalpy 180 kJ/kg. With shaft power of 15 kW supplied to the system, enter −15 kW in the Shaft power delivered field. The enthalpy flow change is 1.5 × (180 − 240) = −90 kW. Required heat duty is −90 + (−15) = −105 kW. Under the selected convention, this means removing 105 kW of heat from the system. The inputs illustrate an energy balance and are not tabulated properties of a particular fluid.

Distinguish an energy quantity in a closed system from an energy transfer rate in steady flow. Energy transferred over a period is power multiplied by duration. Do not treat kJ as kW without specifying time. Inlet and outlet enthalpies must use the same reference and unit. Adding heat leaving the system as a positive heat gain creates a sign error. A zero heat duty does not mean the device produces no work, because enthalpy and work terms may balance. This preliminary calculation cannot adequately represent mixing of multiple streams or changing stored energy using the single inlet steady model.

Frequently asked questions

How do you calculate energy balance?

For example, if a closed system receives 100 kJ of heat and performs 30 kJ of work on its surroundings, total energy changes by 70 kJ. The first law subtracts work done by the system from heat supplied, while this preliminary balance does not resolve separate energy forms or determine process rates.

Calculate with these values