In which of the given three different paths will work done on system be maximum | TestHub

Passage / Comprehension

If the boundary of a system moves by an infinitesimal amount, the work involved is given by:

$d w = - P_{e x t} d V$

For an irreversible process:

$w = - P_{e x t} Δ V$ (where $Δ V = V_{f} - V_{i}$ )

For a reversible process:

$P_{e x t} = P_{in t} \pm d P \approx P_{in t}$

So, for a reversible isothermal process:

$w = - n RT ln \frac{V _{f}}{V _{i}}$

Two moles of an ideal gas undergo isothermal compression along three different paths:

(i) Reversible compression from $P_{i} = 2 ba r$ and $V_{i} = 8 L$ to $P_{f} = 20 ba r$ .

(ii) A single-stage compression against a constant external pressure of $20 ba r$ .

(iii) A two-stage compression consisting initially of compression against a constant external pressure of $10 ba r$ until $P_{g a s} = P_{e x t}$ , followed by compression against a constant pressure of $20 ba r$ until $P_{g a s} = P_{e x t}$ .

In which of the given three different paths will work done on system be maximum :

Options:

Answer:

Solution:

For isothermal compression,

$w = - P_{e x t} Δ V$

Work done on the gas depends on external pressure.

Greater the opposing pressure, greater is the work done on the system.

In path (ii), compression occurs directly against constant external pressure $20 ba r$ , which is the highest pressure acting throughout the process.

Reversible compression (path i) gives minimum work, while two-stage compression (path iii) gives intermediate work.

Hence, maximum work is done in path (ii).

Option (B)

Chemistry - Thermodynamics - I Question with Solution | TestHub

Options:

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