Question

Three sample of the same gas, x, y and z, for which the ratio of specific heats is $\gamma =3/2$ have initially the same volume. The volume of the each sample is doubled by adiabatic process in the case of x, by isobaric process in the case of y and by isothermal process in the case of z. If the initial pressure of the sample of x, y and z are in the ratio $2\sqrt{2}:1:2$ then the ratio of their final pressures is

• A. 2 : 1 : 1
• B. 1 : 1 : 1
• C. 1 : 2 : 1
• D. 1 : 1 : 2

Answer 1

The correct option is B 1 : 1 : 1

For isothermal process, $PV=$constant

For adiabatic process, $P{V}^{\gamma }=$constant

For isobaric process, $P=$ constant

Let initial pressure of y be $P$

Then, final pressure of x=$2\sqrt{2}P\times 2^{-1.5}$$=P$

final pressure of y= initial pressure of y$=P$

final pressure of z=$2P\times .5$$=P$

Thus ratio of final pressures is $1:1:1$