# Calculating work output of an engine, using ideal gas

• lagwagon555
In summary, the problem involves a model Stirling engine using 8.04 × 10–3 mol of ideal gas as the working substance. It operates between a high temperature reservoir at 98.0 °C and a low temperature reservoir at 25.0 °C. The volume of the working substance doubles during each expansion stroke and the engine runs at a rate of 0.7 cycles per second. The question asks for the amount of work done by the engine per cycle. To solve this, one may use the equation W(eng) = Qh - Qc and draw a PV diagram for an idealized Stirling cycle.

## Homework Statement

A model Stirling engine uses n = 8.04 × 10–3 mol of gas (assumed to be ideal) as a working substance. It operates between a high temperature reservoir at TH = 98.0 °C and a low temperature reservoir at Tc = 25.0 °C. The volume of its working substance doubles during each expansion stroke. It runs at a rate of 0.7 cycles per second. Assume the engine is ideal.

How much work does the engine do per cycle?

W(eng) = Qh - Qc

## The Attempt at a Solution

I assume that you have to find the energy input and output by using the temperatures, and the mol of gas, taking into account it's an ideal gas. However, taking the first step is the problem. I have no clue how to work out Qh and Qc, from the given data. Or perhaps there's some other way you have to solve it?

Last edited:
Intuon Theerapong
What does the problem actually ask you to calculate? You don't seem to have included that in the problem statement... does it actually say you need to find the energy input and output, or are you just guessing at that?

I can't believe I forgot to put that question in. I edited the original - sorry about that.

Have you drawn the PV diagram for an idealized Stirling cycle? If not, that would help with figuring out what's going on.

## 1. How do you calculate the work output of an engine using ideal gas?

To calculate the work output of an engine using ideal gas, you can use the equation W = P(V2-V1), where W is work, P is pressure, and V2 and V1 are the final and initial volumes of the gas, respectively. This equation is based on the first law of thermodynamics, which states that the work done by a system is equal to the change in internal energy of the system.

## 2. What is the ideal gas law and how is it used in calculating work output?

The ideal gas law is represented by the equation PV = nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the gas constant, and T is the temperature. This law is used in calculating work output as it relates pressure, volume, and temperature, which are all factors that can impact the work output of an engine.

## 3. What factors can affect the work output of an engine using ideal gas?

There are several factors that can affect the work output of an engine using ideal gas, including the pressure and volume of the gas, the temperature of the gas, and the number of moles of gas present. Additionally, the efficiency of the engine and any external factors, such as friction or heat loss, can also impact the work output.

## 4. How does the work output of an engine using ideal gas compare to the actual work output?

The work output of an engine using ideal gas is often compared to the actual work output to determine the efficiency of the engine. In ideal conditions, the work output calculated using ideal gas should be close to the actual work output. However, in real-world scenarios, the actual work output may be lower due to factors such as mechanical losses and heat loss.

## 5. Can the work output of an engine using ideal gas be increased?

Yes, the work output of an engine using ideal gas can be increased by adjusting the pressure, volume, and temperature of the gas, as well as by improving the efficiency of the engine. However, there are physical limitations to how much the work output can be increased, and it is important to consider the impact on the environment and the cost of these improvements.