In thermodynamics, QH is the total heat energy absorbed by a system from a high-temperature source, often called the “hot reservoir.” It represents the energy input that drives a heat engine, and it’s the starting point for calculating how much useful work that engine can produce. The subscript H stands for “hot,” distinguishing this heat from QC (or QL), which is the heat rejected to a cooler reservoir.
How QH Fits Into a Heat Engine
A heat engine works by moving thermal energy from a hot source to a cold source, converting part of that energy into mechanical work along the way. Picture a simple setup: a hot reservoir at temperature TH, a cold reservoir at temperature TC, and a “working body” (like a gas inside a piston) sitting between them. The working body absorbs heat QH from the hot reservoir, does some work by expanding, then dumps leftover heat QC into the cold reservoir before resetting for the next cycle.
The energy balance for one complete cycle is straightforward. Because the system returns to its starting state after each cycle, there’s no net change in internal energy. That means all the energy has to go somewhere:
Wnet = QH − QC
The net work output equals the difference between the heat absorbed from the hot reservoir and the heat dumped into the cold one. If an engine absorbs 500 joules from its heat source and rejects 300 joules to the cold side, it produces 200 joules of useful work.
Thermal Efficiency and QH
Thermal efficiency measures what fraction of QH actually gets converted into work. The formula is:
η = Wout / QH
This is usually expressed as a percentage. An engine that turns 200 joules of its 500-joule heat input into work has an efficiency of 40%. The remaining 60% exits as waste heat to the cold reservoir. No matter how cleverly you design the engine, you can never reach 100% efficiency. The Kelvin-Planck statement of the second law of thermodynamics says it plainly: no device operating in a cycle can absorb heat from a single reservoir and convert all of it into work. Some energy always has to be rejected to a colder sink. A device that violated this rule would be a perpetual-motion machine, producing W = QH with zero waste heat.
QH in the Carnot Cycle
The Carnot cycle is the idealized benchmark for heat engines, and QH enters during its first step: isothermal expansion. The working gas, already at the temperature of the hot reservoir TH, is placed in contact with that reservoir and allowed to expand slowly. Because the temperature stays constant, all the heat flowing in from the reservoir goes toward pushing the piston outward and doing work. The amount of heat absorbed during this step is QH.
In a Carnot cycle, the relationship between heat and temperature is especially clean. The heat absorbed and rejected are directly proportional to their reservoir temperatures:
QH / TH = QC / TC
This leads to the maximum possible efficiency for any engine operating between two temperatures:
ηCarnot = 1 − TC / TH
Temperatures here must be in Kelvin. An engine running between a hot reservoir at 600 K and a cold reservoir at 300 K could, at best, convert half of QH into work. Real engines always fall short of this limit due to friction, heat leaks, and other irreversibilities.
Units and Sign Conventions
QH is measured in the same units as any other energy quantity. In SI units, that’s joules (J) or kilojoules (kJ). In older engineering contexts, you may also see British thermal units (BTUs) or calories. The quantity itself is simply energy transferred as heat, so the unit depends on the system of measurement being used.
Sign conventions vary by textbook, which can cause confusion. In most engineering thermodynamics courses, heat entering the system is treated as positive. Under this convention, QH is a positive number because energy flows into the working body. Heat leaving the system (QC) is positive when written as a separate output term, so the energy balance reads W = QH − QC with both Q values as positive magnitudes. Some physics texts use a different convention where heat leaving is negative. The physics doesn’t change, but pay attention to which convention your course uses so the signs in your equations stay consistent.
Real-World Sources of QH
Any high-temperature energy source can serve as the hot reservoir that supplies QH. In a coal or natural gas power plant, QH comes from burning fuel inside a boiler, heating water into high-pressure steam. In a nuclear plant, the heat comes from fission reactions in the reactor core. Geothermal power plants tap underground hydrothermal resources where water or steam reaches 300°F to 700°F, using that thermal energy as QH to drive turbines.
Even a car engine follows this pattern. The combustion of gasoline inside the cylinders provides QH. The expanding hot gases push the pistons (producing work), and the remaining heat exits through the exhaust and cooling system as QC. The efficiency of a typical gasoline engine sits around 20 to 30%, meaning most of QH ends up as waste heat rather than motion. That gap between QH and useful work is exactly what thermodynamics predicts, and it’s why engineers spend so much effort pushing operating temperatures higher and waste heat lower.