Courses
Courses for Kids
Free study material
Offline Centres
More
Store Icon
Store
seo-qna
SearchIcon
banner

The temperature of 3 kg of nitrogen is raised from 10C to 100C . Compute the difference in work done if heating were at constant pressure and at constant volume.
( For nitrogen Cp=1400Jkg1K1 & CV=740Jkg1K1)
A. 81000 J
B. 64000 J
C. 49000 J
D. 36000 J

Answer
VerifiedVerified
490.2k+ views
like imagedislike image
Hint:-First find the number of moles in 3kg of nitrogen , then use the formula work done to raise the temperature of n number of moles by ΔTat constant pressure (W=nCpΔT) and also for work done to raise the temperature of n number of moles by ΔTat constant volume (W=nCVΔT).
After finding all the differences by subtracting , this is the required answer.

Complete step-by-step solution:
Work done to raise the temperature from 10C to 100Cat constant pressure W=nCpΔT
Work done to raise the temperature from 10C to 100Cat constant volume W=nCVΔT
Since in both the cases the temperature is increasing by the same degree so change in internal energy for both the cases is the same.
Difference in work done if heating were at constant pressure and at constant volume is given by ΔW
ΔW=nCpΔTnCVΔT
By simplifying the relation we get,
ΔW=n(CpCv)ΔT
We know that (CpCv)=R
(CpCv)=R
R=8.314Jkg1K1
numberofmoles=weightmolarmass
Finding the numbers of moles of nitrogen in 3kg.
n=3kg28gm=3000gm28gm=107.142moles
ΔW=n(CpCv)ΔT (CpCv)=R & R=8.314Jkg1K1
Putting all the values we get,
ΔW=107.142(8.314).(10010)
By solving this we get with
ΔW81000J
Since , the difference in work done if heating were at constant pressure and at constant volume is 81000J.

Hence option (A) is the correct answer.

Note:- Work done to increase the temperature of gases at constant pressure is always greater than the work done to increase the temperature by the same amount of gases at constant volume.
However, in both the cases the temperature is increasing by the same degree so change in internal energy for both the cases is the same.
Latest Vedantu courses for you
Grade 11 Science PCM | CBSE | SCHOOL | English
CBSE (2025-26)
calendar iconAcademic year 2025-26
language iconENGLISH
book iconUnlimited access till final school exam
tick
School Full course for CBSE students
PhysicsPhysics
ChemistryChemistry
MathsMaths
₹41,848 per year
Select and buy