Internal Energy Change Calculator

What is Internal Energy (ΔU)?

Internal energy (U) is the total energy stored within a system. Think of it as all the energy of the tiny particles (atoms and molecules) that make up a substance. This includes their movement (kinetic energy) and the energy stored in their bonds and interactions (potential energy). When we talk about internal energy change (ΔU), we're looking at how this total energy changes during a process, like heating a gas or melting ice.

The First Law of Thermodynamics

The First Law of Thermodynamics is essentially the law of energy conservation applied to heat and work. It states that energy cannot be created or destroyed, only transferred or changed from one form to another. For a system, any change in its internal energy (ΔU) comes from the heat (Q) added to or removed from it, and the work (W) done by or on it.

• ΔU = Q - W: This is the most common form, where Q is heat added to the system, and W is work done *by* the system.
• Energy is conserved: The total energy of the universe remains constant.
• Path-independent: The change in internal energy only depends on the initial and final states of the system, not how it got there.

Internal Energy of Ideal Gases

For an ideal gas, a simplified model of a gas, the internal energy depends almost entirely on its temperature. This is because in an ideal gas, we assume there are no forces between the gas particles, so their potential energy is zero. Therefore, any change in internal energy for an ideal gas is directly related to a change in its temperature.

• ΔU = nCvΔT: This formula calculates the internal energy change, where 'n' is the number of moles, 'Cv' is the molar heat capacity at constant volume, and 'ΔT' is the change in temperature.
• Temperature-dependent: Internal energy of an ideal gas changes only with temperature.
• Volume/Pressure independent: It does not depend on changes in volume or pressure, only temperature.

Internal Energy During Phase Changes

When a substance undergoes a phase change (like ice melting into water, or water boiling into steam), its internal energy changes even though its temperature stays constant. This energy is used to break or form the bonds between molecules, changing the substance's physical state. This hidden energy is called latent heat.

• Constant Temperature: During a phase change, the temperature of the substance remains the same.
• Energy for Structure: The energy added or removed goes into changing the arrangement and interactions of molecules.
• Latent Heat: This is the specific amount of energy required per unit mass for a substance to change phase.
• Different for each change: The latent heat for melting/freezing (fusion) is different from that for boiling/condensing (vaporization).