Polytropic Process

• Calculate total work done in a polytropic process.

In a polytropic process both heat and work transfers take place. It follows the equation

$Pv^{n} = c$

where n is called the index of process or polytropic index.
Work done, $W = \dfrac{p_1 V_1 - p_2 V_2}{n-1} = \dfrac{mR(T_1- T_2)}{n-1}$ Change in internal energy, $\Delta U = mC_v (T_2- T_1)$ $Q = \left(\dfrac{n - \gamma}{n - 1}\right) mC_V (T_2 - T_1)$ Depending upon various values of n, there will be following cases:

• n = 0, constant pressure (Isobaric) process

• n = 1, constant temperature (Isothermal) process

• n = $\gamma$ , reversible adiabatic process

• n = $\infty$ ,constant volume (Isochoric) process

Solved Example:

72-6-01

If the value of n = 0 in the equation pv$^n$ = C, then the process is called: (AFCAT EKT Mech Paper I- Set 02/2016)

Correct Answer: C

Solved Example:

72-6-02

The value of n = 1 in the polytropic process indicates it to be: (UPSSSC JE Mech 2016 Paper 2)

Solution:
When n= 1 in the equation PV$^n$ = constant, it reduces to PV = constant, which is Boyle's law where temperature is kept constant. Hence n=1 represents an isothermal process.

Correct Answer: B

Solved Example:

72-6-03

If value of n is infinitely large in a polytropic process pV$^n$ = C, then the process is known as constant: (UPPSC AE Mech 2019)

Correct Answer: A

Solved Example:

72-6-04

During polytropic process:

Correct Answer: D

Solved Example:

72-6-05

A fluid at 0.7 bar occupying 0.09 m$^3$ is compressed reversibly to a pressure of 3.5 bar according to pv$^n$ = constant. The fluid is then heated reversibly at constant volume until the pressure is 4 bar; the specific volume is then 0.5 m$^3$/kg. A reversible expansion according to the law pv$^{1.6}$ = constant restores the fluid to its initial state. Calculate the net work of the cycle.

Correct Answer: C

Solved Example:

72-6-06

A mass of gas at initial pressure of 30 bar, and with an internal energy of 1500kJ, is contained in a well-insulated cylinder of volume 0.1m$^3$. The gas is allowed to expand behind a piston until its internal energy is 1300 kJ, the law of expansion is pv$^2$ = constant. Calculate the final pressure.

Correct Answer: A

Solved Example:

72-6-07

A fluid at a pressure of 3 bar and with specific volume of 0.18m$^3$/kg, contained in a cylinder behind a piston expands reversibly to a pressure of 0.6 bar according to the law p = $\dfrac{C}{V^2}$, where C is a constant. The work done by the fluid on the piston is:

Correct Answer: A

Solved Example:

72-6-08

Properties of substances like pressure, temperature and density, in thermodynamic coordinates are:

Correct Answer: B

Solved Example:

72-6-09

Which of the following quantities is not the property of the system: (SJVNL JE Mech 2018)

Correct Answer: D

Solved Example:

72-6-10

According to Avogadro's law, for a given pressure and temperature, each molecule of a gas:

Correct Answer: D

Solved Example:

72-6-11

Which of the following is not the intensive property? (SSC JE ME Paper 11- March 2021 Morning)

Solution:
An intensive property is a bulk property, meaning that it is a physical property of a system that does not depend on the system size or the amount of material in the system. Another way of looking at it is, if two containers having same pressure are combined the resultant pressure will remain same. The same can be stated regarding temperature and density. However, the heat content will be sum of two individual heat contents, hence it is not an intensive property.

Correct Answer: D

Solved Example:

72-6-12

Which of the following items is not a path function: (BPSC AE NE 2012- Part 5)

Correct Answer: D

Solved Example:

72-6-13

Heat and work are: (GATE ME 2011)

Correct Answer: B

Solved Example:

72-6-14

Which of the following parameters is constant for a mole for most of the gases at a given temperature and pressure:

Correct Answer: B

Solved Example:

72-6-15

For an ideal gas with constant values of specific heats, for calculation of the specific enthalpy: (GATE ME 2015- Shift I)

Correct Answer: A

Solved Example:

72-6-16

The area under the temperature-entropy curve (T-s curve) of any thermodynamic process represents: (Based on JKSSB JE ME 2015)

Correct Answer: C

Solved Example:

72-6-17

A mixture of gas expands from 0.03 m$^3$ to 0.06 m$^3$ at a constant pressure of 1 MPa and absorbs 84 kJ of heat during the process. The change in internal energy of the mixture is: (ISRO RAC 2018)

Correct Answer: B

Solved Example:

72-6-18

Heating wet steam at constant temperature is heating it at constant:

Correct Answer: B

Solved Example:

72-6-19

Intensive property of a system is one whose value:

Correct Answer: B

Solved Example:

72-6-20

The index of compression n tends to reach ratio of specific heats $\gamma$ when:

Correct Answer: D

Solved Example:

72-6-21

Change in enthalpy of a system is the heat supplied at: (UPSSSC JE Mech 2016- Paper 2)

Correct Answer: A

Solved Example:

72-6-22

The term N.T.P. stands for:

Correct Answer: C

Solved Example:

72-6-23

In an isothermal process, the internal energy of gas molecules: (ISRO VSSC Tech Asst. Mech Feb 2015)

Correct Answer: C

Solved Example:

72-6-24

Work done is zero for the following process:

Correct Answer: D

Solved Example:

72-6-25

In a non-flow reversible process for which p = (- 3V+ 15) $\times$ 10$^5$ N/m$^2$,V changes from 1 to 2 m$^3$. The work done will be about: (ESE Mech 2013- Paper 1)

Correct Answer: C

Solved Example:

72-6-26

In a free expansion process:

Correct Answer: C

Solved Example:

72-6-27

If a fluid expands suddenly into vacuum through an orifice of large dimension, then such a process is called:

Correct Answer: A

Solved Example:

72-6-28

Which of the following processes is irreversible process: (VIZAG MT Mech 2017)

Correct Answer: C

Solved Example:

72-6-29

For a thermodynamic process to be reversible, the temperature difference between hot body and working substance should be:

Correct Answer: A

Solved Example:

72-6-30

Minimum work in compressor is possible when the value of adiabatic index n is equal to:

Correct Answer: B

Solved Example:

72-6-31

A gas is compressed in a cylinder by a movable piston to a volume one-half its original volume. During the process 300 kJ heat left the gas and internal energy remained same. The work done on gas in Nm will be: (TANGEDCO AE EC 2018)

Correct Answer: B

Solved Example:

72-6-32

For reversible adiabatic process, change in entropy is: (BPSC AE ME 2019- Part 5)

Correct Answer: C

Solved Example:

72-6-33

Change in enthalpy in a closed system is equal to heat transferred if the reversible process takes place at constant: (UPPSC AE Mech 2019- Paper II)

Correct Answer: A