**A) Find w12, the work done on the gas as it expands from state 1 to state 2. Express the work done in terms of Po and…**

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## Question “A) Find w12, the work done on the gas as it expands from state 1 to state 2. Express the work done in terms of Po and…”

state 2.

Express the work done in terms of Po and Vo

B) Find W23 , the work done on the gas as it cools from state 2 to

state 3.

Express your answer in terms of Po and Vo.

C) Find W34, the work done on the gas as it is compressed from

state 3 to state 4.

Express your answer in terms of Po and Vo.

D) Find W41, the work done on the gas as it is heated from state 4

to state 1.

Express your answer in terms of Po and Vo .

E)What is Wnet, the total work done on the gas during one

cycle?

Express your answer in terms of Po and Vo .

F) When the gas is in state 1, its temperature is T1. Find the

temperature T3 of the gas when it is in state 3. (Keep in mind that

this is an ideal gas.)

Express T3 in terms of T1.

The diagram shows the pressure and volume of an ideal gas during

one cycle of an engine. As the gas proceeds from state 1 to state

2, it is heated at constant pressure. It is then cooled at constant

volume, until it reaches state 3. The gas is then cooled at

constant pressure to state 4. Finally, the gas is heated at

constant volume until it returns to state 1.

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## Answer

This problem was solved by the use of a thermodynamic process as well as an ideal gas equation.

Find the area below the *P*– *V* curve to find the work done on gas from states 1 through 2. State 2 to state 3. State 3 to sate 4. And state 4 to state 1. Add all the work done, i.e.

to find the total amount of work that was done on the gas in one cycle.

The last part of the equation is ideal gas equation. Find temperature for state 3.

Here is the equation of state for ideal gas:

Here, P is pressure, V is volume, n the number of moles and R is universal gas constant. T is temperature of ideal gas.

Calculate the work that gas does in a thermodynamic process by using:

Gas’s work depends on its initial and final states, as well as the path.

**(A)**

Calculated as follows:

Substitute

for

and

for

.

is required to replace

in the equation.

**(B)**

Calculated as follows:

During the transition from state 2 to 3 the volume of the gas remains constant. Substitute 0 for *DV*.

The gas is therefore cooled from state 2 to 3 at a temperature of 0.

**(C)**

According to the following calculation, the work on the gas from states 3 and 4 was:

Substitute

for

and

for

.

is required to replace

in the equation.

**(D)**

According to the following calculation, the work on the gas from states 4 to 1 was:

During the transition from state 4 to 1., the volume of the gas remains constant. Substitute 0 for *DV*.

The gas cools down from state 4 to 1 at a temperature of 0.

**(E)**

One cycle of gas work is:

Substitute

for

,

for

, 0 for

and

.

**(F)**

The following formula calculates the temperature at which the gas is in its state 1:

Substitute HTMLmedia_tag_32$ for

or HTMLmedia_tag_34$ for

.

The following formula calculates the temperature at which the gas is in 3 state:

Substitute HTMLmedia_tag_38$ for

, and HTMLmedia_tag_40$ for

.

to get the value of *nR*.

.

Part A – Ans

**The gas expansion from state 1 into state 2 was**

.

## Conclusion

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