An ideal gas has an adiabatic exponent gamma. It contracts according to the law PV equals to alpha, where 'a' is a positive constant. For the process, the bulk modulus of the gas is?
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Explanation:
The process is given as P=αV
⟹ PV
−1
=α=constant
Comparing with PV
m
=constant we get m=−1
Given : V
1
=V
o
V
2
=ηV
o
⟹ P
1
=αV
o
and P
2
=αηV
o
Change in internal energy ΔU=
γ−1
R
×n(T
2
−T
1
)=
γ−1
P
2
V
2
−P
1
V
1
⟹ ΔU=
γ−1
[αηV
o
(ηV
o
)−αV
o
(V
o
)]
=
γ−1
αV
o
2
(η
2
−1)
Work done W=
1−m
P
2
V
2
−P
1
V
1
∴ W=
1−(−1)
[αηV
o
(ηV
o
)−αV
o
(V
o
)]
=
2
αV
o
2
(η
2
−1)
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