First Law of Thermodynamics Calculator

Apply energy conservation: the change in internal energy of a closed system, the steady-flow energy equation for a turbine, compressor, nozzle or heat exchanger, and Q = m cp dT.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

The first law says energy is conserved. For a closed system the change in internal energy equals the heat added minus the work done by the system. Heat in is positive and work out is positive.

For a steady-flow device the heat added minus the work done equals the mass flow rate times the change in specific enthalpy, kinetic energy and potential energy. Choose which quantity you want to find.

For heating or cooling a flow with no change of state the heat is the mass flow rate times the specific heat times the temperature change.

Formulas used

  • \Delta U = Q - W
  • \dot Q - \dot W = \dot m\left[\Delta h + \dfrac{\Delta V^2}{2} + g\Delta z\right]
  • \dot Q = \dot m\,c_p\,\Delta T

Worked example

With the default numbers in the calculator above:

  1. Change in internal energy: 300.00 kJ

Change the numbers in the calculator to see the full working, every step, for your own case.

A second worked example

A different case, with these numbers: Mass of the gas (closed system, optional, 0 to skip) 2 kg.

  1. Change in internal energy: 300.00 kJ
  2. Temperature change of the gas (constant specific heat): 208.91 K

Common questions

What is the sign convention?

Heat is positive when it goes into the system, and work is positive when the system does work on its surroundings.

Where do I get the enthalpy?

From steam or refrigerant tables. The property tables calculator on this site has them.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Standard thermodynamics texts (first law for closed systems and control volumes).

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