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An ideal gas is taken from the state A (...

An ideal gas is taken from the state A (pressure P, volume V) to the state B (pressure `p//2`, volume 2V) along a straight line path in the P-V diagram. Select the correct statement (s) from the following :

A

The work done by the gas in the process A to B. exceeds the work that would be done by it, if system were taken along the isotherm.

B

In the T-V diagram, the path AB becomes a part of a hyperbola

C

In the p-T diagram, the path AB becomes a part of a hyperbola

D

In going goind A to B, the temperature T of the gas first decreases to a miniumum value and then increase.

Text Solution

Verified by Experts

The correct Answer is:
a
`W=(1)/(2)(rho+(rho)/(2))V=(3)/(4)rhoV=0.75rhoV`

`W_(iso)=RTxx2.3026"log"_(10)((2V)/(V))=0.693 rhoV`
Thus, statement (a) is correct.
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Knowledge Check

  • An ideal gas is taken from the state A (pressure P, volume V) to the state B (pressure P/2, volume 2V) along a straight line path in the P-V diagram. Select the wrong statement from the following:

    A
    The work done by the gas in the process A to B exceeds the work that would be done by if the system were taken from A to B along the isotherm.
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    C
    In the P-T diagram, the path AB becomes a part of hyperbola.
    D
    In going from A to B, the temperature T of the gas first increases to a maximum value and then decreases.

  • An ideal gass is taken from state A (Pressuer P, VolumeV) to the state B ( Pressure P/2, Volume 2V) along a stright line path in PV diagram as shown in the adjacent figure . Select the correct statement (s) among the following .

    A
    The work done by gas in the process A to B exceeds the work that
    would be done by gas in if the system were taken from A to B along the isotherm.
    B
    In The T- V diagram, the path AB become part of parabola.
    C
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  • An ideal gas is taken form the state A(P,V) to the state B((P)/(2),2V) along a straight line path in the P-V diagram. Select the correct options (i) The work done by the gas in the process A to B exceeds the work that would be done by it if the system were taken from A to B along the isotherm (ii) In the T-V diagram, the path AB becomes part of a hyperbola (iii) In the P-T diagram, the path AB becomes part of a hyperbola (iv) In going from A to B, the temperature T of the first increases to maximum value and then decreases

    A
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    B
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    C
    (iii),(iv)
    D
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