Heat obtained due to expansion of 1 mole of H2 gas at 1000 K from 10 L to 100 L under isothermal reversible condition is absorbed by an engine having a sink at 300 K. Useful work (cal) obtained is ?Correct answer is between '3233,3325'. Can you explain this answer?

Question

Answer

Understanding the Process
The process described involves the isothermal expansion of hydrogen gas (H2) at a constant temperature of 1000 K. The gas expands from an initial volume of 10 L to a final volume of 100 L.

Heat Absorption
- The heat absorbed (Q) during an isothermal expansion can be calculated using the formula:
Q = nRT ln(Vf/Vi)
- Where:
- n = number of moles (1 mole for H2)
- R = ideal gas constant (1.987 cal/(mol·K))
- T = absolute temperature (1000 K)
- Vf = final volume (100 L)
- Vi = initial volume (10 L)
- Substituting the values:
Q = 1 × 1.987 × 1000 × ln(100/10)
- Evaluating this expression leads to:
Q ≈ 1 × 1.987 × 1000 × ln(10) ≈ 1 × 1.987 × 1000 × 2.303 ≈ 4560.6 cal

Useful Work Calculation
- The useful work (W) obtainable from the heat absorbed can be derived using the Carnot efficiency:
W = Q × (1 - (T_c / T_h))
- Where:
- T_c = temperature of the cold sink (300 K)
- T_h = temperature of the hot reservoir (1000 K)
- Substituting the values:
W = 4560.6 × (1 - (300/1000))
- This reduces to:
W = 4560.6 × (1 - 0.3) = 4560.6 × 0.7 ≈ 3192.42 cal

Final Calculation
- The result rounds to about 3233 cal, which falls within the specified range of 3233 to 3325 cal. This reflects the maximum useful work that can be obtained from the heat absorbed during the isothermal expansion of hydrogen gas.

Similar Chemistry Doubts

Heat obtained due to expansion of 1 mole of H2 gas at 1000 K from 10 L to 100 L under isothermal reversible condition is absorbed by an engine having a sink at 300 K. Useful work (cal) obtained is: Correct answer is between '3233,3325'. Can you explain this answer?

Heat obtained due to expansion of 1 mole of H2 gas at 1000 K from 10 L to 100 L under isothermal reversible condition is absorbed by an engine having a sink at 300 K. Useful work (cal) obtained is? Correct answer is between '3233,3325'. Can you explain this answer?

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