# Thermodynamics Fun: Is Net Work = Change in Q for Brayton Cycle?

• sportsrules
In summary, the first law of thermodynamics states that the change in internal energy is equal to the heat added to the system plus the work done by the system. In the case of a Brayton cycle using helium gas, it is reasonable to have the net work and the change in heat for the cycle to be equal, as the first law of thermodynamics suggests. However, since a Brayton cycle is not isolated, this may not always be the case. It is important to calculate the work done and heat evolved for each step in the cycle in order to accurately analyze the system.
sportsrules
For a brayton cycle on a pressure and temperature diagram, using helium gas, is it reasonable to have the net work for the cycle and the change in Q for the cycle to come out to be equal to each other?

i thought the first law of thermodynamics said "change in work is equal to change in heat"

so yeah it is reasonable. and i just worked some brayton cycle problems for homework, and yeah that's what i had

audi476 said:
i thought the first law of thermodynamics said "change in work is equal to change in heat"

so yeah it is reasonable. and i just worked some brayton cycle problems for homework, and yeah that's what i had

First law of Thermodynamics

$$\Delta U = q + w$$

Or in differential form

$$dU = dq + dw$$

In an ISOLATED system, $$\Delta U = 0$$. A Brayton cycle, however, is not isolated. Actually its not even closed. So offhand I would not expect the net work to be the same as the net heat evolved. I would however, calculate the work done and heat evolved through all 4 steps of the cycle for an ideal gas. You have two isobars and two isoentropes (constant entropy).

Last edited:

## 1. What is a Brayton Cycle?

The Brayton Cycle is a thermodynamic cycle that describes the operation of a gas turbine engine. It consists of four processes: isentropic compression, constant pressure heat addition, isentropic expansion, and constant pressure heat rejection.

## 2. How is net work calculated for a Brayton Cycle?

The net work for a Brayton Cycle is calculated by taking the difference between the work output from the turbine and the work input to the compressor. This can be represented by the equation: Net Work = WTurbine - WCompressor.

## 3. Is Net Work always equal to the change in heat for a Brayton Cycle?

No, the net work for a Brayton Cycle is not always equal to the change in heat. This is because the Brayton Cycle is an open system, meaning that heat can enter or leave the system during the constant pressure heat addition and rejection processes.

## 4. How does the efficiency of a Brayton Cycle compare to other thermodynamic cycles?

The efficiency of a Brayton Cycle is generally higher than other thermodynamic cycles, such as the Otto Cycle or Diesel Cycle. This is because the Brayton Cycle operates at higher temperatures, allowing for more efficient energy conversion.

## 5. What are some real-world applications of a Brayton Cycle?

The Brayton Cycle is commonly used in gas turbine engines, such as those used in aircraft and power plants. It is also used in other applications, such as refrigeration and air conditioning systems, as well as in some types of rocket engines.

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