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An ideal gasundergoes isothermal compression from 5 m3 against a constant external pressure of 4 Nm-2  Heat relesed in this process is used to increase the temprature of 1 mole of Al . If molar heat capacity of Al is 24 J mol-1 K-1,the temperture of Al increases by:

  • Option 1)

    \frac{3}{2}K

     

  • Option 2)

    \frac{2}{3}K

  • Option 3)

    1K

  • Option 4)

    2K

Answers (1)

best_answer

 

Work Done for Irreversible Isothermal Expansion of an ideal gas -

W= -P_{ext}\left ( V_{f} -V_{i}\right )

- wherein

P_{ext} may be equal to P_{f} or may not be equal to P_{f}, but work done is always calculated by P_{ext}

 

As we have learned in isothermal expansion.

The work done on isothermal irreversible for ideal gas

= -Pext   (V2 - V1)

= -4N/m2  (1m3 - 5m3)

=16 Nm

For an isothermal process for ideal gas

\Delta U = 0 , q = -W

= -16 Nm

= -16 J

Heat used to increase temperature of Al

16 J = 1 x 24 \frac{J}{mol. K} \times \Delta T

\Delta T = \frac{2}{3}K


Option 1)

\frac{3}{2}K

 

Option 2)

\frac{2}{3}K

Option 3)

1K

Option 4)

2K

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