Calculate change in internal energy, heat transfer, work, pressure, or volume using the first law and constant-pressure PΔV relationships.

Change in Internal Energy Calculator

General (First Law)
Constant Pressure (PΔV work)

Enter any 2 values to calculate the missing variable

Change in Internal Energy Formula

The calculator uses the first law of thermodynamics. In the General mode, work is treated as work done on the system, so positive work increases internal energy.

Δ U = Q + W
  • ΔU = change in internal energy
  • Q = heat transferred to the system
  • W = work done on the system

For the General mode, the calculator can solve any one missing value if you enter the other two:

Q = Δ U - W
W = Δ U - Q

In the Constant Pressure mode, the calculator assumes the only work is pressure-volume work. The formula used is:

Δ U = Qₚ - PΔ V
  • ΔU = change in internal energy
  • Qp = heat transfer at constant pressure
  • P = pressure
  • ΔV = change in volume
  • PΔV = pressure-volume work term

For the Constant Pressure mode, the calculator can also rearrange the equation to solve for heat transfer, pressure, or change in volume:

Qₚ = Δ U + PΔ V
P = (Qₚ - Δ U) / (Δ V)
Δ V = (Qₚ - Δ U) / (P)

The calculator converts energy values to joules, pressure values to pascals, and volume values to cubic meters before applying the formulas. The result is then converted back to the unit you selected.

Energy, Pressure, and Volume Conversions

These are the base conversions used in the calculations.

Quantity Unit Equivalent in base unit
Energy 1 kJ 1000 J
Energy 1 cal 4.184 J
Energy 1 kcal 4184 J
Pressure 1 kPa 1000 Pa
Pressure 1 bar 100,000 Pa
Pressure 1 atm 101,325 Pa
Volume 1 L 0.001 m³
Volume 1 cm³ 0.000001 m³

Sign Meaning for Internal Energy Results

Value Meaning
Positive ΔU The system’s internal energy increased.
Negative ΔU The system’s internal energy decreased.
Positive Q Heat is added to the system.
Negative Q Heat leaves the system.
Positive W in General mode Work is done on the system.
Negative W in General mode Work is done by the system.

Examples

Example 1: General first law calculation

Suppose heat transfer is 500 J and work done on the system is -120 J. Find the change in internal energy.

Δ U = Q + W
Δ U = 500 + (- 120) = 380 J

The change in internal energy is 380 J.

Example 2: Constant pressure calculation

Suppose heat transfer at constant pressure is 2.50 kJ, pressure is 100 kPa, and change in volume is 3.0 L. Find the change in internal energy.

Convert the values used in the pressure-volume term:

100 kPa = 100000 Pa
3.0 L = 0.003 m³
PΔ V = 100000 × 0.003 = 300 J

Since 2.50 kJ equals 2500 J:

Δ U = Qₚ - PΔ V = 2500 - 300 = 2200 J

The change in internal energy is 2200 J, or 2.20 kJ.

FAQ

What sign convention does this calculator use for work?

In General mode, work is entered as work done on the system. That means positive work increases internal energy and negative work decreases internal energy. The formula is ΔU = Q + W.

Why is PΔV subtracted in the constant pressure formula?

At constant pressure, expansion uses energy to do pressure-volume work. With the calculator’s convention, the internal energy change is calculated as ΔU = Qp – PΔV. If volume increases, ΔV is positive and the PΔV term reduces ΔU. If volume decreases, ΔV is negative and subtracting PΔV increases ΔU.

Why do pressure and volume multiply to give energy?

Pressure has units of pascals, and volume has units of cubic meters. Since 1 Pa equals 1 N/m², Pa·m³ becomes N·m, which is the same as a joule. That is why PΔV is an energy term.