All Courses
Explore Courses UPSC Exam UPSC Test Series Free Notes EduRev Infinity Get the App Login Join for Free
Sign in Open App
JEE Exam  >  JEE Questions  >  Calculate the max. work done by system in an ... Start Learning for Free
SaveJoin the Discussion on the App
Calculate the max. work done by system in an irreversible (single step) adiabatic expansion of 2 mole of a polyatomic gas from 300K and pressure 10 atm to 1 atm.( γ = 1.33).?
Clear all your JEE doubts with EduRev
Verified Answer
Calculate the max. work done by system in an irreversible (single step...
Ans.


This question is part of UPSC exam. View all JEE courses
Most Upvoted Answer
Calculate the max. work done by system in an irreversible (single step...
Max Work Done by System in Irreversible Adiabatic Expansion


Given:


  • Number of moles of gas (n) = 2

  • Initial temperature (T1) = 300 K

  • Initial pressure (P1) = 10 atm

  • Final pressure (P2) = 1 atm

  • Ratio of specific heats (γ) = 1.33



Calculating the Max Work Done:


Step 1: Determining the Initial Volume (V1):

We can use the ideal gas law to find the initial volume of the gas:
PV = nRT

Substituting the given values:
V1 = (nRT1) / P1
V1 = (2 * 0.0821 * 300) / 10
V1 = 4.923 L

Step 2: Determining the Final Volume (V2):

Since the process is irreversible, we cannot directly use the adiabatic equation P1V1^γ = P2V2^γ. Instead, we use the relationship between temperature and volume for an adiabatic process:
T1V1^(γ-1) = T2V2^(γ-1)

Substituting the given values:
300 * (4.923)^(1.33-1) = T2 * V2^(1.33-1)
T2 * V2^0.33 = 300 * 4.923^0.33
V2^0.33 = (300 * 4.923^0.33) / T2

Step 3: Applying the Ideal Gas Law to Find Final Volume:

Using the ideal gas law, we can express the final volume in terms of pressure and temperature:
PV = nRT

Substituting the given values:
1 * V2 = 2 * 0.0821 * T2
V2 = (2 * 0.0821 * T2) / 1

Step 4: Combining Equations to Solve for Final Volume:

Substituting the expression for V2 from Step 3 into the equation from Step 2:
((2 * 0.0821 * T2) / 1)^0.33 = (300 * 4.923^0.33) / T2

Simplifying the equation:
(2 * 0.0821 * T2) / 1 = (300 * 4.923^0.33) / T2^(0.33)
T2^1.33 = (300 * 4.923^0.33) / (2 * 0.0821)
T2 = [(300 * 4.923^0.33) / (2 * 0.0821)]^(1/1.33)
T2 ≈ 468.3 K

V2 = (2 * 0.0821 * 468.3
Explore Courses for JEE exam

Similar JEE Doubts

A gaseous sample is generally allowed to do only expansion/compression type of work against its surroundings. The work done in case of an irreversible expansion (in the intermediate stages, of expansion/compression the states of gases are not define d). The work done can be calculated usingdW = NextdVwhile in case of reversible process the work done can be calculated using dw = PdV where P is pressure of gas at some intermediate stages. Like for an isothermal reversible process.Since d w = P d V so magnitude of worked one can also be calculated by, calculating the area under the PV curve of the reversible process in PV diagram.Q.If four identical samples of an ideal gas initially at similar state (P0, Vo, T0) are allowed to expand to double their volumes by four different processes..I : by isothermal irreversible process II : by reversible process having equation P2V = constant III : by reversible adiabatic process IV: by irreversible adiabatic expansion against constant external pressure.Then in the graph shown the final state is represented by four different points then, the correct match can be

A gaseous sample is generally allowed to do only expansion/compression type of work against its surroundings. The work done in case of an irreversible expansion (in the intermediate stages, of expansion/compression the states of gases are not define d). The work done can be calculated usingdW = NextdVwhile in case of reversible process the work done can be calculated using dw = PdV where P is pressure of gas at some intermediate stages. Like for an isothermal reversible process.Since d w = P d V so magnitude of worked one can also be calculated by, calculating the area under the PV curve of the reversible process in PV diagram.Q.Two samples (initially under same states) of an ideal gas are first allowed to expand to double their volume using irreversible isothermal expansion against constant external pressure, then samples are returned back to their original volume first by reversible adiabatic process and second by reversible process having equation PV2 = constant then

A gaseous sample is generally allowed to do only expansion/compression type of work against its surroundings. The work done in case of an irreversible expansion (in the intermediate stages, of expansion/compression the states of gases are not define d). The work done can be calculated usingdW = NextdVwhile in case of reversible process the work done can be calculated using dw = PdV where P is pressure of gas at some intermediate stages. Like for an isothermal reversible process.Since d w = P d V so magnitude of worked one can also be calculated by, calculating the area under the PV curve of the reversible process in PV diagram.Q.An ideal gaseous sample at initial state i (P0V0T0) is allowed to expand to volume 2V0 using two different process; in the first process the equation of process is PV2= K1 and in second process the equation of the process is PV = K2 .Then

Top Courses for JEEView all

Top Courses for JEE

Calculate the max. work done by system in an irreversible (single step) adiabatic expansion of 2 mole of a polyatomic gas from 300K and pressure 10 atm to 1 atm.( γ = 1.33).?
Question Description
Calculate the max. work done by system in an irreversible (single step) adiabatic expansion of 2 mole of a polyatomic gas from 300K and pressure 10 atm to 1 atm.( γ = 1.33).? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Calculate the max. work done by system in an irreversible (single step) adiabatic expansion of 2 mole of a polyatomic gas from 300K and pressure 10 atm to 1 atm.( γ = 1.33).? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Calculate the max. work done by system in an irreversible (single step) adiabatic expansion of 2 mole of a polyatomic gas from 300K and pressure 10 atm to 1 atm.( γ = 1.33).?.
Solutions for Calculate the max. work done by system in an irreversible (single step) adiabatic expansion of 2 mole of a polyatomic gas from 300K and pressure 10 atm to 1 atm.( γ = 1.33).? in English & in Hindi are available as part of our courses for JEE. Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of Calculate the max. work done by system in an irreversible (single step) adiabatic expansion of 2 mole of a polyatomic gas from 300K and pressure 10 atm to 1 atm.( γ = 1.33).? defined & explained in the simplest way possible. Besides giving the explanation of Calculate the max. work done by system in an irreversible (single step) adiabatic expansion of 2 mole of a polyatomic gas from 300K and pressure 10 atm to 1 atm.( γ = 1.33).?, a detailed solution for Calculate the max. work done by system in an irreversible (single step) adiabatic expansion of 2 mole of a polyatomic gas from 300K and pressure 10 atm to 1 atm.( γ = 1.33).? has been provided alongside types of Calculate the max. work done by system in an irreversible (single step) adiabatic expansion of 2 mole of a polyatomic gas from 300K and pressure 10 atm to 1 atm.( γ = 1.33).? theory, EduRev gives you an ample number of questions to practice Calculate the max. work done by system in an irreversible (single step) adiabatic expansion of 2 mole of a polyatomic gas from 300K and pressure 10 atm to 1 atm.( γ = 1.33).? tests, examples and also practice JEE tests.
Explore Courses for JEE exam

Top Courses for JEE

Explore Courses

Suggested Free Tests

Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Get App
© EduRev
Education Revolution
Signup to see your scores go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup