An ideal gas NTP is enclosed in a adiabatic vertical cylinder having area of cross section A = 27 cm^3, between two light movable pistons as shown in the figure. Spring with force constant k = 3700 N/m is in a relaxed state initially. Now the lower piston is moved upwards a height h/2, h being the length of gas column. It is observed that the upper piston moves up by a distance h/16. Find h taking γ for the gas to be 1.5. Also find the final temperature of gas
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Answers
Answer:
2.37p
Step-by-step explanation:
NTP: To=0oC=273KPo=1bar=105Pa
Final volume, Vf=[h+16h−2h]A=169hA=169Vo
Using PVγ=K
PoPf=(169VoVo)1.5
⟹Pf=2.37Po
Now Pf=Po+16AKh where k=3700N/mA=27×10−4m2
2.37P
NTP: T
o
=0
o
C=273KP
o
=1bar=10
5
Pa
Final volume, V
f
=[h+
16
h
−
2
h
]A=
16
9
hA=
16
9
V
o
Using PV
γ
=K
P
o
P
f
=(
16
9
V
o
V
o
)
1.5
⟹P
f
=2.37P
o
Now P
f
=P
o
+
16A
Kh
where k=3700N/mA=27×10
−4
m
2
2.37P
o
=P
o
+
16(27×10
−4
)
3700(h)
⟹h=1.6m
Also, TV
γ−1
=constant
273
T
f
=(
16
9
V
o
V
o
)
.
5
⟹T
f
=364K
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