First Law Energy Calculator

Calculator Inputs

Use heat added to the system as positive. Use work done by the system as positive.

Process Name

Calculation Mode

Decimal Places

Heat Transfer Q

Work W

Internal Energy Change ΔU

Mass m

Initial Specific Energy u₁

Final Specific Energy u₂

Energy Unit

Mass Unit

Plotly Graph

The chart compares heat transfer, work, and internal energy change for the submitted case.

Formula Used

First law for a closed system:

ΔU = Q - W

Q = ΔU + W

W = Q - ΔU

ΔU = m(u₂ - u₁)

u₂ = u₁ + (Q - W) / m

Meaning of symbols: ΔU is internal energy change, Q is heat transfer, W is work, m is mass, and u is specific internal energy.

Sign rule: Heat entering the system is positive. Work done by the system is positive.

How to Use This Calculator

Select the calculation mode based on the unknown you want to find.
Enter process details and choose suitable energy and mass units.
Provide the required known values for Q, W, ΔU, m, u₁, or u₂.
Click Calculate to show the result above the form.
Review the result cards, balance check, and graph for interpretation.
Use the CSV or PDF buttons to export your result summary.

Example Data Table

Case	Q (kJ)	W (kJ)	ΔU (kJ)	m (kg)	u₁ (kJ/kg)	u₂ (kJ/kg)
Heated gas expansion	120	35	85	2.0	200	242.5
Cooling compression	-45	-15	-30	1.5	310	290
Rigid tank heating	60	0	60	3.0	150	170

Frequently Asked Questions

1. What does the first law of thermodynamics state?

It states that energy is conserved. For a closed system, the change in internal energy equals heat added to the system minus work done by the system.

2. What sign convention does this calculator use?

This page uses heat added to the system as positive and work done by the system as positive. Always keep the same convention throughout your calculation.

3. Can I solve for heat, work, or internal energy change?

Yes. The calculator lets you solve for ΔU, Q, W, or final specific internal energy, depending on which known values you enter.

4. When should I use ΔU = m(u₂ - u₁)?

Use that form when mass and specific internal energy values are known. It is especially useful for tabulated thermodynamic property problems.

5. Does this calculator convert units automatically?

No. It labels your selected units clearly, but you should enter values in a consistent unit system before calculating.

6. Why is there an energy balance check?

The balance check shows Q - W - ΔU. A value near zero indicates the submitted values satisfy the first-law relation.

7. Is this calculator useful for lab reports?

Yes. It provides labeled results, an example table, a chart, and export options that help summarize thermodynamics exercises and lab work.

8. What types of systems fit this calculator best?

It is best for closed-system first-law problems, such as piston-cylinder devices, rigid tanks, and many introductory thermodynamics examples.