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Question

When an ideal gas at pressure p, temperature T and volume V is isothermally compressed to V/n, its pressure becomes pi. If the gas is compressed adiabatically to Vn, its pressure becomes pa. The ratio pi/pa is (γ=CpCV)

A
1
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B
n
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C
nγ
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D
n1γ
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Solution

The correct option is B n1γ
For isothermal process,
pV= constant.
Therefore piVi=pV
or piVn=pV
or pi=np .....(i)
For adiabatic process, pVγ= constant.
Therefore
pa(Va)γ=pVγ
or pa(Van)γ=pVγ
or pa=nγp
From Eqs. (i) and (ii), we get
pipa=nnγ=n(1γ)

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