Consider the reversible isothermal expansion of an ideal gas in a closed system at two different temperatures \(T_{1} \& T_{2}\left(T_{1}<T_{2}\right)\). The correct graphical depiction of the dependence of work done(w) on the final volume(v).

JEE Main · 2019 · 09 Jan 2019 · Shift 1 · Chemical Thermodynamics

Consider the reversible isothermal expansion of an ideal gas in a closed system at two different temperatures

T_{1} & T_{2} (T_{1} < T_{2})

. The correct graphical depiction of the dependence of work done(w) on the final volume(v).

(A)(see structure)
(B)(see structure)
(C)(see structure)
(D)(see structure)
✓ Correct

Answer: (D)

Solution

For a reversible isothermal expansion the work done relates to volume as

w = - n R T ln \frac{V}{V _{i}}

, so against

ln V

it is a straight line whose slope is set by

- n R T

. Since

T_{2} > T_{1}

, the

T_{2}

line is the steeper of the two, and because the higher-temperature path also starts from a larger volume its intercept sits more negative. The depiction showing the

T_{2}

line both steeper and shifted below the

T_{1}

line is the correct one.

JEE Main · 2019 · 09 Jan 2019 · Shift 1 · Single correct option

Practise more: all JEE Main PYQs on Chemical Thermodynamics →

JEE Main · 2019 · 09 Jan 2019 · Shift 1 · Chemical Thermodynamics

Solution

More JEE Main questions on Chemical Thermodynamics