Internal Energy

The Internal Energy calculator computes the total change in internal energy of a system based on heat exchanged (q) and the work (w) done by or on the system.

INSTRUCTIONS: Choose units and enter the following:

• (q) Heat exchanged between a system and its surroundings
• (w) Work done by or on the system

Internal Energy (ΔU): The calculator returns the total change in internal energy of a system in units of (Joules).  However this can be automatically converted to compatible units via the pull-down menu.

The Math / Science

The Internal energy^[1] equation calculates the amount of energy is absorbed or released by the system. This equation is also known as the first law of thermodynamics. The first law of thermodynamics is often called the Law of Conservation of Energy^[3].This law suggests that Energy can be changed from one form to another, but it cannot be created or destroyed. The total amount of energy and matter in the Universe remains constant, merely changing from one form to another. The First Law of Thermodynamics (Conservation) states that energy is always conserved, it cannot be created or destroyed. In essence, energy can be converted from one form into another.  The formula for Internal energy is:

      ΔU = q+w

where:

• ΔU = the total change in internal energy of a system
• q = the heat exchanged between a system and its surroundings 
• w = the work^[2] done by or on the system

When work is done by the system then work will be negative and positive when work is done on to the system. When heat is negative, then it is released from the system. 

Chemistry Calculators

• R - Gas Constant: 8.3144626181532 J/(K⋅mol)
• Boyle's Law Calculator:  P₁ • V₁ = P₂ • V₂
• Charles Law Calculator: V₁• T₂ = V₂ • T₁
• Combined Gas Law Calculator:   P•V / T= k
• Gay-Lussac Law:  T₁•P₂ =T₂•P₁ 
• Ideal Gas Law: P•V = n•R•T
• Bragg's Law:   n·λ = 2d·sinθ
• Hess' Law:  ΔH⁰_rxn=ΔH⁰_a+ΔH⁰_b+ΔH⁰_c+ΔH⁰_d
• Internal Energy: ΔU = q + ω 
• Activation Energy:  E_a = (R*T₁⋅T₂)/(T₁ - T₂) ⋅  ln(k₁/k₂)
• Arrhenius Equation:  k = Ae^E_a/(RT)
• Clausius-Clapeyron Equation:  ln(P₂/P₁) = (ΔH_vap)/R * (1/T₁ - 1/T₂)
• Compressibility Factor: Z = (p*V_m)/(R*T)
• Peng-Robinson Equation of State:  p = (R*T)/(V_m - b) - (a*α)/(V_m² + 2*b*V_m - b²)
• Reduced Specific Volume:  v_r = v/(R* T_cr / P_c)
• Van't Hoff Equation:  ΔH⁰ = R * ( -ln(K₂/K₁))/ (1/T₁ - 1/T₂)

Work and Energy Calculators

• Internal Energy of an Ideal Gas
• Internal Energy
• Change in Internal Energy
• Work
• R - Gas Constant
• Ideal Gas Law
• Sackur-Tetrode Equation
• First Law of Thermodynamics

Related Topics

• Enthalpy
• Work
• Heat

Supplement Material

• Khan Academy: First law of thermodynamics / internal energy
• HyperPhysics: Internal Energy
• UC Davis: Internal Energy

References

[1]https://en.wikipedia.org/wiki/First_law_of_thermodynamics

[2]Whitten, et al. 10th Edition. Pp.571

[3]https://en.wikipedia.org/wiki/Conservation_of_energy