Consider two containers A and B containing identical gases
at the same pressure, volume and temperature. The gas in
container A is compressed to half of its original volume
isothermally while the gas in container B is compressed to
half of its original value adiabatically. The ratio of final
pressure of gas in B to that of gas in A is
(a) 2γ⁻¹ (b) (1/2)γ⁻¹
(c) (1/1-γ)²
(d) (1/γ-1)²
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Consider the P−V diagram shown for the container A and container B.
Both the process involves compression of the gas
(i) Isothermal compression (Gas A) (during 1→2)
P
1
V
1
=P
2
V
2
⟹P
0
(2V
0
)
γ
=P
2
(V
0
)
γ
⟹P
0
(2V
0
)=P
2
(V
0
)
(II) Adiabatic compression (Gas B) (during 1→2)
P
1
V
1
γ
=P
2
V
2
γ
⟹P
0
(2V
0
)
γ
=P
2
(V
0
)
γ
⟹P
2
=(
V
0
2V
0
)
γ
P
0
=(2)
γ
P
0
Hence
(P
2
)
A
(P
2
)
B
= Ratio of final pressure =
2P
0
(2)
γ
P
0
=2
γ−1
where, γ is the ratio of specific heat capacities for the gas.
solution
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