Q. 175.0( 2 Votes )

Consider the cyclic process ABCA, shown in the figure, performed on a sample 2.0 mol of an ideal gas. A total of 1200 J of heat is withdrawn from the sample in the process. Find the work done by the gas during the part BC.



Answer :

Given


Heat extracted from the system ΔQ=-1200J


(negative sign is because heat is extracted from the system)


Number of moles of the gas n=2.0



From the graph we can write


TA=300K


TB=500K


VA=VC


We know that work done by the gas is given as


ΔW=PΔV


Where ΔV =change in volume


P =pressure


So, work done along line CA will be zero, as VA=VC.


Thus, total work done will be


ΔW=WAB+WBC


WAB = P(VB-VA)


But we know that ideal gas equation is


PV=nRT


Where n= number of moles


R=gas constant


T=temperature


PΔV=nRΔT


Thus, we can write WAB = P(VB-VA) = nR(TB-TA)


ΔW= nR(TB-TA) + WBC


From first law of thermodynamics, we know that,


ΔQ=ΔU+ΔW


Where ΔQ=heat supplied to the system


ΔU=change in internal energy


ΔW=work done by the system


Process ABCA is a cyclic process. The system is brought back to its initial state. Since internal energy is a state function, change in internal energy will be zero.


So, ΔU=0.


So, first law becomes


ΔQ=ΔW


ΔQ= nR(TB-TA) + WBC


We know that R=8.31J/K mol


WBC =ΔQ- nR(TB-TA)


= -1200 - 2×8.31× (500-300)


=-1200 – 3324


=-4524J


Thus, work done along path BC =-4524J


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
JEE Advanced Level Questions of NLM48 mins
Work done in Thermodynamic ProcessFREE Class
Microsporogenesis & Megasporogenesis49 mins
NEET 2021 | Transcription - An important Topic62 mins
Meselson and Stahl experiment49 mins
DNA Fingerprinting42 mins
Interactive Quiz on Sexual Reproduction in flowering plants44 mins
Pedigree chart58 mins
MCQs of Ecology for NEET52 mins
Application of Biotechnology48 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses
RELATED QUESTIONS :