Constant volume heat rejection is the process of removing heat from the working fluid while its volume stays fixed. In Thermodynamics II, it shows up in idealized cycle analysis, especially the Diesel and Dual cycles.
Constant volume heat rejection is the part of a thermodynamic cycle where heat leaves the working fluid but the volume does not change. In Thermodynamics II, this is usually discussed as an idealized process in air-standard Diesel and Dual cycle analysis, not as a perfectly literal engine event.
The easiest way to picture it is on a pressure-volume diagram. Since volume stays fixed, the path is a vertical line. As heat is rejected, the temperature drops and the pressure falls too, because the gas is losing internal energy while it cannot expand or contract.
That fixed-volume condition makes the math cleaner. With no boundary work, the process energy balance simplifies, so you can focus on how much heat is leaving the system and how the pressure and temperature respond. For ideal gases with constant specific heats, this is often handled with straightforward property relationships instead of a long work calculation.
In the Diesel cycle, heat rejection happens after the expansion stroke, when the working fluid has already done useful work and needs to return to the initial state. In the Dual cycle, the same idea appears at the end of the cycle after the constant-volume and constant-pressure heat addition steps have raised the state of the gas.
A common mistake is to mix up constant volume heat rejection with constant pressure heat rejection. They are not the same process, and the diagrams look different. Constant pressure heat rejection would be a horizontal line on a P-V diagram, while constant volume heat rejection is vertical. That difference changes the work term and changes how you compute cycle performance.
Constant volume heat rejection shows up whenever you analyze idealized gas power cycles and want to compare how efficiently they convert heat into work. In Thermodynamics II, you use it to close the loop on Diesel and Dual cycles and figure out state properties after the expansion process.
It also matters because it changes the thermal efficiency calculation. The amount of heat rejected, along with how that rejection compares to heat addition, affects the net work output of the cycle. If you can identify the heat rejection process correctly, you can write the right energy balances and avoid carrying the wrong work term into your efficiency result.
This term also helps explain why cycle shape matters. A cycle with heat rejection at fixed volume behaves differently from one with heat rejection during a pressure or temperature change, and those differences show up in pressure traces, state-point calculations, and comparisons of Mean Effective Pressure.
In problem sets, this concept is often the step that separates a correct cycle sketch from a fully solved cycle analysis. If you know where the heat leaves the system and what stays constant, the rest of the calculations become much easier to organize.
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view galleryDiesel Cycle
The Diesel cycle is the most common place you see constant volume heat rejection in Thermodynamics II diagrams and calculations. After the expansion process, the cycle returns to the initial state by rejecting heat, and that last step is often modeled as fixed volume. If you can track that closing process, you can usually finish the cycle analysis without losing the state order.
Dual Cycle
The Dual cycle combines constant volume and constant pressure heat addition, but it still ends with heat rejection that returns the working fluid to the starting state. Constant volume heat rejection helps close the cycle and makes the pressure-volume plot easier to read. It is a good checkpoint for figuring out which processes add heat and which ones remove it.
Heat Rejection
Heat rejection is the broader category, and constant volume heat rejection is one specific version of it. In this case, the working fluid gives off heat without changing volume, so there is no boundary work during the process. That makes it easier to isolate the energy leaving the system and connect it to cycle efficiency.
thermal efficiency
Thermal efficiency depends on how much heat goes in compared with how much heat comes out, so constant volume heat rejection affects the denominator of the efficiency ratio. In Diesel and Dual cycle problems, once you find the rejected heat at fixed volume, you can calculate net work and then efficiency. A small mistake in the rejection step can throw off the whole result.
A problem set or quiz question will usually ask you to identify the process on a P-V diagram, find the heat rejected, or use the state relation at constant volume to solve for pressure or temperature. You may also need to explain why no boundary work is done during this step. If the cycle is Diesel or Dual, this is often one of the last states you calculate before finding net work, thermal efficiency, or Mean Effective Pressure.
When you see a vertical line on the P-V plot, read it as fixed volume first, then ask whether heat is entering or leaving. For rejection, pressure and temperature both drop. That is the move that keeps you from swapping it with a constant pressure process or accidentally adding the wrong sign in the energy balance.
These get mixed up because both describe heat leaving the system, but the constraint is different. Constant volume heat rejection means the volume stays fixed, so the process is a vertical line on a P-V diagram and no boundary work is done. Constant pressure heat rejection would keep pressure fixed instead, which changes the diagram shape and the work term.
Constant volume heat rejection means heat leaves the working fluid while the volume stays fixed.
On a P-V diagram, this process appears as a vertical line because pressure changes but volume does not.
In Thermodynamics II, you usually see it in ideal Diesel and Dual cycle analysis when the cycle is closing.
Because the volume does not change, there is no boundary work during this process.
If you confuse it with constant pressure heat rejection, your diagram, energy balance, and efficiency result can all come out wrong.
It is the step in a cycle where heat is removed from the working fluid while the volume stays fixed. In ideal Diesel and Dual cycle analysis, it is usually the closing process that brings the system back toward its initial state. On a P-V diagram, it shows up as a vertical downward line.
It looks like a vertical line because the volume does not change. As heat is rejected, pressure drops, so the line goes downward. That visual cue is one of the fastest ways to tell it apart from constant pressure heat rejection, which would be horizontal.
Boundary work depends on a change in volume, and this process has none. Since the system does not expand or compress, the work term is zero. That is why the energy balance focuses on the heat leaving the gas and the drop in internal energy.
You use it to find the final state after expansion and before the cycle repeats. With constant volume, you can relate pressure and temperature changes using the ideal-gas state relation and the cycle equations you have already built from the other processes. It is often the last step before calculating net work and thermal efficiency.