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+50×10100×10−4=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
=100×10−4×20×10−2=2×10−3 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
=15×104×2×10−3=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.