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प्रश्न
Answer the following question.
One mole of an ideal gas is compressed from 500 cm3 against a constant pressure of 1.2 × 105 Pa. The work involved in the process is 36.0 J. Calculate the final volume.
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उत्तर
Given:
Initial volume (V1) = 500 cm3
External pressure (Pext) = 1.2 × 105 Pa
Work (W) = 36.0 J
To find: Final volume (V2)
Formula: W = - Pext Δ V = - Pext (V2 - V1)
Calculation: Initial volume (V1) = 500 cm3 = 0.5 dm3
External pressure (Pext) = 1.2 × 105 Pa = 1.2 bar
Work (W) = 36.0 J = 36.0 J × `(1 "dm"^3 "bar")/(100 "J")` = 0.360 dm3 bar
Now, from formula,
W = - Pext Δ V = - Pext (V2 - V1)
∴ 0.360 dm3 bar = - 1.2 bar × (V2 - 0.5 dm3)
∴ `(0.360 "dm"^3 "bar")/(1.2 "bar")` = - (V2 - 0.5 dm3)
∴ 0.3 dm3 = - V2 + 0.5 dm3
∴ V2 = 0.2 dm3 = 200 cm3
The final volume (V2) = 200 cm3.
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