Thermal Efficiency Calculator

Thermal efficiency (ͷ) is fundamentally defined as the ratio of net work output ($W$) to the total thermal energy input ($Q_{in}$). According to the conservation of energy, the net work is also equal to the difference between the heat added and the heat rejected ($Q_{out}$). Therefore, the general formula is expressed as ͷ = $W / Q_{in}$, or alternatively, ͷ = $1 - (Q_{out} / Q_{in})$. For ideal reversible systems like the Carnot engine, thermal efficiency depends entirely on the absolute temperatures of the hot source ($T_h$) and cold sink ($T_c$), calculated as ͷ_{rev} = $1 - (T_c / T_h)$. All temperature inputs for theoretical maximum efficiency must be converted to absolute scales such as Kelvin or Rankine.

Let us calculate the thermal efficiency of a power plant heat engine that receives a heat input ($Q_{in}$) of 2,000 kJ/kg and rejects a waste heat output ($Q_{out}$) of 1,100 kJ/kg to the environment. First, find the net work done ($w$) per unit mass: $w = Q_{in} - Q_{out} = 2,000 - 1,100 = 900\text{ kJ/kg}$. Next, apply the thermal efficiency formula: ͷ = $w / Q_{in} = 900 / 2,000 = 0.45$. Converting this decimal into a percentage yields a thermal efficiency of 45%, meaning nearly half of the supplied thermal energy is successfully transformed into useful mechanical work.

Always ensure your temperature values are in absolute units (Kelvin or Rankine) when calculating theoretical limits like Carnot efficiency, as Celsius and Fahrenheit scales will yield incorrect thermodynamic ratios. Pay close attention to mass-specific versus total energy units; mixing up Joules with Joules per kilogram is a common error in cycle analysis. Finally, remember that no real-world engine can exceed the thermal efficiency of an idealized reversible cycle operating between the same two temperature boundaries.