Question

The $P-V$ diagram of a system undergoing thermodynamic transformation is shown in figure. The work done by the system and heat given to the system in going from $A\to B\to C$ is $30\text{J}$ and $40\text{J}$ respectively. The change in internal energy between $A$ and $C$ is

• A. $70\text{J}$
• B. $10\text{J}$
• C. $-70\text{J}$
• D. $-10\text{J}$

Answer 1

The correct option is B $10\text{J}$

Given,

$W_{AB}+W_{BC}=30\text{J}$
$Q_{AB}+Q_{BC}=40\text{J}$
Applying 1st law of thermodynamics for process AB,
$\begin{array}{}{Q}_{AB}=\Delta U_{AB}+W_{AB}& \text{(1)}\end{array}$
Simillarly applying 1st law of thermodynamics for process BC,
$\begin{array}{}{Q}_{BC}=\Delta U_{BC}+W_{BC}& \text{(2)}\end{array}$
Adding $\left(1\right)$ and $\left(2\right)$,
$Q_{AB}+Q_{BC}=\Delta U_{AB}+W_{AB}+\Delta U_{BC}+W_{BC}$
$40=(\Delta U_{AB}+\Delta U_{BC})+30$
Here $\Delta U_{AB}+\Delta U_{BC}=\Delta U_{AC}$
$\Rightarrow \Delta U_{AC}=40-30=10\text{J}$