wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Figure shows a cylindrical container containing oxygen gas and closed by a piston of mass 50 kg. Piston can slide smoothly in the cylinder. Its cross sectional area is 100 cm2 and atmospheric pressure is 105 Pa. Some heat is supplied to the cylinder so that the piston is slowly displaced up by 20 cm.
Find the amount of heat supplied to the gas.

A
1050 J
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
750 J
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
105 J
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
1505 J
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A 1050 J
Let us assume the given gas is ideal in nature.
From the figure we can say that, piston is open to atmosphere, thus the gas is under a constant pressure given as
Pgas=Patm+MgA
from the data given in the question,
Pgas=105+50×10100×104=105+5×104=15×104 Pa ........(1)
When heat is supplied ,it is given that the piston moves out by Δx=20 cm, thus increment is its volume
ΔV=A×Δx
=100×104×20×102=2×103 m3
From (1) we can say that the pressure is constant, so the process is isobaric.
work done by gas during isobaric process is given by
W=PgasΔV
=15×104×2×103=300 J
Since, W=nRΔT=PgasΔV
we can say that, nRΔT=300 J .........(2)
Thus heat supplied in raising the temperature by ΔT is given by
ΔQ=nCPΔT
For a diatomic ideal gas, CP=7R2
ΔQ=n(72R)ΔT
From (2) we get,
ΔQ=n(7R2)×300nR=72×300=1050 J
Thus, option (a) is the correct answer.

flag
Suggest Corrections
thumbs-up
0
similar_icon
Similar questions
View More
Join BYJU'S Learning Program
Join BYJU'S Learning Program
CrossIcon