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The equation of a state of a gas is give...

The equation of a state of a gas is given by `p(V-b)=nRT`. If 1 mole of a gas is isothermally expanded from volume V and 2V, the work done during the process is

A

(a) `RT ln|(2V-b)/(V-b)|`

B

(b) `RT ln|(V-b)/(V)|`

C

(c) `RT In|(V-b)/(2V-b)|`

D

(d) `RT In|(V)/(V-b)|`

Text Solution

Verified by Experts

The correct Answer is:
A
`W=int_V^(2V)pdV`
`=int_V^(2V)((nRT)/(V-b))dV`
`=nRT In((2V-b)/(V-b))`
Put `n=1`,
`:.` `W=RT In((2V-b)/(V-b))`
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Knowledge Check

  • One mole of an ideal gas expands isothermally to double its volume at 27^(@)C . The work done by the gas is nearly

    A
    `2760 cal`
    B
    `414 cal`
    C
    `1380 cal`
    D
    `600 cal`

  • A gas expands under constant pressure P from volume V_(1) to V_(2) The work done by the gas is

    A
    `P(V_(2)-V_(1))`
    B
    `P(V_(1)-V_(2))`
    C
    `P(V_(1)^(lambda)-V_(2)^(lambda))`
    D
    `P(V_(1)V_(2))/(V_(2)-V_(1))`

  • A sample of gas expands from volume V_1 to V_2 . The amount of work done by the gas is greatest, when the expansion is

    A
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    B
    Equal in all cases
    C
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