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1 kg of a gas does 20 kJ of work and receives 16 kJ of heat when it is expanded between two states. A second kind of expansion can be found between the initial and final state which requires a heat input of 9 kJ. The work done by the gas in the second expansion is :

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13 kJ

32 kJ

-4 kJ

5 kJ

answer is D.

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Detailed Solution

For first kind of expansion-
$\begin{array}{l} Δ W = 20 K J \\ Δ Q = 16 K J \\ ∴ Δ U = Δ Q - Δ W = - 4 K J \end{array}$

Since, U is a state function. Therefore, value of DU in both expansions remain same.
Thus, for second expansion
$Δ U = - 4 K J, Δ Q = 9 K J$

$∴$ By first law of the thermodynamics
$Δ W = Δ Q - Δ U = 13 K J$

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