A gas undergoes a thermodynamic cycle consisting of three processes:

## Expert Answer

## General guidance

A thermodynamic cycle is a series of processes which returns system to initial conditions. The thermodynamic process is a polytropic process following certain relation between pressure and volume. Work done can be determined by finding the area under the pressure-volume diagram.

First law of thermodynamics: When there is any energy transfer takes place to or from the system then the system internal energy changes.

An ideal thermodynamic process whose deviation from the thermodynamic equilibrium is infinitesimal at any point of time during the process is called a quasi-static process.

Any quasi equilibrium expansion or compression process can be described by the relation,

Here, pressure is , volume is , and constant is .

According to the value of the constant the process changes,

: Isobaric process (Constant pressure)

: Isothermal process (Constant temperature)

: Isochoric process (Constant volume)

A closed system boundary work for a quasi-static process can be calculated using the formula,

Here, initial volume is and final volume is .

First law to the piston cylinder arrangement:

Here, *Q* is heat transfer, *W* is work transfer, is the kinetic energy, is the potential energy, and *dU* is change in internal energy.

If the work is done on the system then consider the value as negative, if the work is done by the system then consider the value as positive.

If heat transfer is positive then heat addition takes place during the process and if heat transfer is negative then heat rejection takes place during the process.

## Step-by-step

### Step 1 of 4

Process 1-2:

Calculate the work done in the process using the following equation:

Here, the initial pressure is , the initial volume is , and the final volume is .

Substitute for , for , and for .

Calculate the final pressure using the following relation:

Substitute for , for , and for .

Explanation | Hint for next step

Work done in process 1-2 is calculated and pressure at state 2 is calculated.

[Common mistake]

Writing incorrect unit for the pressure is a common mistake.

### Step 2 of 4

Calculate the work done in process 2-3.

Here, the pressure and volume at state 2 are and and the volume at state 3 is .

Substitute for , for , and for .

Therefore, the work done in the process2-3 is .

Explanation | Hint for next step

Work done in process 2-3 is calculated.

[Common mistake]

Writing incorrect unit for the work transfer and neglecting the negative sign is a common mistake.

### Step 3 of 4

Calculate the change in internal energy in the process 2-3.

Calculate the heat transfer from energy balance equation.

Therefore, the heat transfer in process 2-3 is .

Explanation | Hint for next step

Heat transfer in process 2-3 is calculated.

### Step 4 of 4

Since the process 3-1 is a constant volume process the work done in the process is zero.

Calculate the work energy transfer for the whole cycle.

Since

Therefore, the cycle is power cycle.

Thermodynamic Cycle is power cycle.

Explanation

Using work done for the whole cycle the type of cycle is determined.

### Answer

Therefore, the work done in the process2-3 is .

Therefore, the heat transfer in process 2-3 is .

Thermodynamic Cycle is power cycle.