Question

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

• A. $32\text{kJ}$
• B. $5\text{kJ}$
• C. $-4\text{kJ}$
• D. $13\text{kJ}$

Answer 1

The correct option is D $13\text{kJ}$

Let the two states be $\text{A}\text{and}\text{B}$, then,

Applying $1^{st}$ law of thermodynamics,

$\Delta Q=W_{AB}+\Delta U$

$\Rightarrow 16\text{kJ}=20\text{kJ}+\Delta U$

$\Rightarrow \Delta U=-4\text{kJ}$

As the internal energy is a state function, so in the second process also $\Delta U=-4\text{kJ}$

Applying $1^{st}$ law of thermodynamics,

$\Delta Q=\Delta U+\Delta W$

$\Rightarrow \Delta W=\Delta Q-\Delta U=9\text{kJ}-(-4\text{kJ})$

$\Rightarrow \Delta W=13\text{kJ}$

Hence, option $\left(\text{D}\right)$ is correct.