The pressure volume work for an ideal gas can be calculated by using the expression $w = - \int_{v}^{v_{1}} p_{e x} d V$ . The work can also be calculate from the $p V - p l o t$ by using the area under the curve within the specified limits. When an ideal gas is compressed (a) reversibly or (b) irreversibly from volume $V_{1}$ to $V_{f}$ . Choose the correct option.

w (r e v e r s i b l e) = w (i r r e v e r s i b l e)

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w (r e v e r s i b l e) < w (i r r e v e r s i b l e)

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w (r e v e r s i b l e) = - w (i r r e v e r s i b l e)

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w (r e v e r s i b l e) = w (i r r e v e r s i b l e) + p_{e v} △ V

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Solution

The correct option is B $w (r e v e r s i b l e) < w (i r r e v e r s i b l e)$
Work done is the area under the $P - V$ curve. It can be seen in the curve above that the area under the $P - V$ curve for irreversible compression of the gas is more than the area under the curve for reversible compression.
Thus, work done for irreversible compression is more than that for reversible compression.

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Similar questions

The pressure-volume work for an ideal gas can be calculated by using the expression $W = \int_{V_{i}}^{V_{f}} p_{e x} d V$ . The work can also be calculated from the pV-plot by using the area under the curve within the specified limits. When an ideal gas is compressed (a) reversibly or (b) irreversibly from volume $V_{i} t o V_{f}$ . Choose the correct option.
(a) W (reversible) = W (irreversible)
(b) W (reversible) < W (irreversible)
(c) W (reversible) = W (irreversible)
(d) W (reversible) = W (irreversible) $+ p_{e x} . Δ V$

Q. The pressure-volume work for an ideal gas can be calculated by using the expression W =

\int P . d V

. The work can also be calculated from P-V diagram by using the area under the curve within the specified limits. When an ideal gas is compressed (i) reversibly or (ii) irreversibly from volume

V_{i}

V_{f}

, choose the correct option about word done in the two processes.

For an ideal gas, the work of reversible expansion under isothermal condition can be calculated by using the expression $W = - n R T l n \frac{V_{f}}{V_{i}}$ . A sample containing 1.0 mol of an ideal gas is expanded isothermally and reversible to ten times of its original volume, in two separate experiments. The expansion is carried out at 300 K and at 600 K respectively. Choose the correct option.
(a) Work done at 600 K is 20 times the work done at 300 K
(b) Work done at 300 K is twice the work done at 600 K
(c) Work done at 600 K is twice the work done at 300 K
(d) $Δ$ U = 0 in both cases