# Work by an ideal gas in a thermodynamic cycle

• merbear
In summary, the problem involves finding the work done by two moles of an ideal gas as it undergoes a thermodynamic cycle consisting of an isothermal expansion, an isobaric compression, and an isochoric pressure increase. Using the equations pv=nRT and W=pdv, we can find the work done for the isothermal expansion from point A to B, but may need additional information to find the work done for the isobaric compression from point B to C.
merbear
1. Homework Statement

Two moles of an ideal gas are carried around the thermodynamic cycle shown in Fig. 18-29. The cycle consists of (1) an isothermal expansion A to B at a temperature of 700 K, with the pressure at A given by pA = 9 atm; (2) an isobaric compression B to C at PC = 4 atm; and (3) an isochoric pressure increase C A. What work is done by the gas per cycle? (See attached picture)

2. Homework Equations

pv=nRT

W=pdv

P=nRT/V

3. The Attempt at a Solution

W=nRT*ln(v2/v1)

For Pa:
9 atm= [2 mol*(.08205784 L*atm/k*mol)*700K]/V2

For Pb:

4 atm= [2 mol*(.08205784 L*atm/k*mol)*700K]/V1

V2/V1= 4/9

W=nRT(ln(4/9)) = 93.16 J (for A to B)

Here is where I got stuck. I can't seem to find the work for B to C without having variables in the answer. Once I can find the work from B to C I can add the work quantities to find the total (and ignore the value for C to B because the total work with no volume change is zero).

Any help in finding work from B to C would be appreciated.

Thank you
1. Homework Statement

2. Homework Equations

3. The Attempt at a Solution

#### Attachments

• 18-25alt.gif
8.7 KB · Views: 586
What is the pressure at C? What is the volume at C?

You can use PV=nRT to find the volume at point A and C
Then, pluge into the formula W=nRT*ln(V2/V1)
Final subtract it with the area below that triangla W - 3*101325*(V2-V1)

## What is an ideal gas?

An ideal gas is a theoretical concept in thermodynamics that describes a gas that follows certain assumptions, such as having no intermolecular forces and being composed of infinitesimally small particles. It is used as a simplified model for real gases in many thermodynamic calculations.

## What is a thermodynamic cycle?

A thermodynamic cycle is a series of thermodynamic processes that occur in a closed system and ultimately return the system to its original state. It is often represented on a pressure-volume diagram and is used to analyze the energy transfer and work done in a system.

## How is work calculated in an ideal gas in a thermodynamic cycle?

In an ideal gas, work is calculated by the equation W = P∆V, where P is the pressure and ∆V is the change in volume of the gas. This equation is based on the work done by the gas on its surroundings or vice versa during a process.

## What is the First Law of Thermodynamics?

The First Law of Thermodynamics states that energy cannot be created or destroyed, but it can be transferred or converted from one form to another. In the context of an ideal gas in a thermodynamic cycle, this law means that the change in the internal energy of the gas is equal to the amount of heat added to the gas minus the work done by the gas.

## What is the significance of work done by an ideal gas in a thermodynamic cycle?

The work done by an ideal gas in a thermodynamic cycle represents the energy transfer and conversion within the system. It can also provide insights into the efficiency of the system and the amount of useful work that can be obtained from the gas. Understanding the work done by an ideal gas is crucial in designing and optimizing thermodynamic processes.

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