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

An ideal monoatomic gas is confined in a cylinder by a spring-loaded piston of area of cross-section 8×103m2. Initially, the gas is at 300 K and occupies a volume of 2.4×103m3 and the spring is in its relaxed state as shown in figure. The gas is heated by a small electric heater until the piston moves out slowly by 0.1 m. The force constant of the spring is 8000 N m1, atmospheric pressure is 1×105Nm2. Find the heat supplied by the heater. The piston is massless and no friction exits between the piston and the cylinder. Neglect the heat loss through the lead wires of heater. The heat capacity of the heater coil is negligible.
811461_743bcc863ad84f1895d1731a5052430c.png

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

The correct option is C 720 J
Solution:
The final pressure on the gas =atm pressure +pressure due to compression of spring
P2=Patm+kxA
P2=105+8000×0.18×103=2×105Nm2
The final volume,
V2=V1+xA=2.4×103+0.1×8×103=3.2×103m3
Applying
P1V1T1=P2V2T2

T2=P2V2T1P1V1
T2=2×105×3.2×103×300105×2.4×103=800K.
Heat supplied by the heater is used for expansion of the gas, increasing its temperature and storing potential energy in the spring.
Heat supplied =PΔV+nCvΔT+12kx2=105[0.8×103]+P1V1RT1CvΔT+12kx2
=80+105×2.4×1032×300×32×2×500+12×8000×0.1=720J


Hence C is the correct option

flag
Suggest Corrections
thumbs-up
0
similar_icon
Similar questions
View More
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Thermodynamic Devices
PHYSICS
Watch in App
Join BYJU'S Learning Program
CrossIcon