Question

A mole of ideal gas undergoes a two-step reversible process (A-B and B-C). The pressure at points A and C is the same. Select the correct statement: Image

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Answer

The correct answers are: C and D.

Calculations:

  1. Determining Volume at Point ( A ):

    $$ V_{A} = \frac{nRT_{A}}{P_{A}} $$

    Given:

    • ( n = 1 ) mole
    • ( R = 0.0821 ) L·atm·K(^{-1})·mol(^{-1})
    • ( T_{A} = 100 ) K
    • ( P_{A} = 1 ) atm

    Therefore:

    $$ V_{A} = \frac{1 \times 0.0821 \times 100}{1} = 8.21 \text{ L} $$

  2. Determining Volume at Point ( B ):

    $$ V_{B} = \frac{nRT_{B}}{P_{B}} $$

    Given:

    • ( T_{B} = 600 ) K
    • ( P_{B} = 3 ) atm

    Therefore:

    $$ V_{B} = \frac{1 \times 0.0821 \times 600}{3} = 16.42 \text{ L} $$

  3. Comparing Volumes ( V_{B} ) and ( V_{A} ):

    Since ( V_{B} > V_{A} ), expansion occurs.

  4. Volume at ( B ) in liters:

    $$ V_{B} = 16.42 \text{ L} $$

Conclusion:

  • C: The volume increases, indicating an expansion.
  • D: The volume at point ( B ) is ( 16.42 ) liters.

Hence, the correct answers are C and D.


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