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Standard XI

Chemistry

Work Done in Isothermal Reversible Process

The graph giv...

Question

The graph given below shows the total work done in an expansion when the state of an ideal gas is changed reversibly and isothermally from $(P_{i}, V_{i})$ to $(P_{f}, V_{f})$ . Compare the work done in the above case with that carried out against a constant external pressure $P_{f}$ .

(i) Area $A B V_{f} V_{i}$ represents total work done for a reversible isothermal expansion from $(P_{i}, V_{i})$ to $(P_{f}, V_{f})$ .
(ii) Area $C B V_{f} V_{i}$ represents work done against a constant pressure $P_{f}$ .

work (i) = work (ii)

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work (i) > work (ii)

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work (i) < work (ii)

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Cannot be defined

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Solution

The correct option is B work (i) > work (ii)
Work done = Area under the P-V curve

As seen from the graph, area under the P-V curve in case (i) which is an isothermal reversible expansion, is greater than the area under P-V curve in case (ii) which is a irreversible expansion.
Hence work (i)> work(ii)

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Similar questions

Q. The graph given below shows the total work done in an expansion when the state of an ideal gas is changed reversibly and isothermally from

(P_{i}, V_{i})

(P_{f}, V_{f})

. Compare the work done in the above case with that carried out against a constant external pressure

P_{f}

(i) Area

A B V_{f} V_{i}

represents total work done for a reversible isothermal expansion from

(P_{i}, V_{i})

(P_{f}, V_{f})

.
(ii) Area

C B V_{f} V_{i}

represents work done against a constant pressure

P_{f}

Q. An ideal gas is subjected to an isothermal expansion such that its volume changes from

V_{i}

V_{f}

and pressure from

P_{i}

P_{f}

. The work done by the gas is:

Q. Calculate the work done in joules when

3

moles of an ideal gas at

27^{\circ} C

expands isothermally and reversibly from

10

atm to

1

atm (

1 a t m = 1.013 \times 10^{5} N m^{- 2}

). What will be the work done if the expansion is against the constant pressure of

1

atm?

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