Question

A thermodynamic process is shown in the following figure. The pressure and volumes corresponding to some points in the figure are:
$P_A=3\times {10}^{3}Pa,V_A=2\times {10}^{-3}{m}^3$
$P_B=3\times {10}^{4}Pa,V_D=2\times {10}^{-3}{m}^3$
In process $AB$, $600J$ of heat is added to the system and in the process $BC$, $200J$ of heat is added to the system. The change in internal energy of the system in the process $AC$ would be:

• A. $560J$
• B. $800J$
• C. $600J$
• D. $640J$

Answer 1

Answer: (B)

$800J$

$Q_{AC}=Q_{AB}+Q_{BC}=600+200=800J$

For AB process, $\Delta V=0\therefore W_{AB}=0$

$W_{BC}=-P\Delta V$

$=-P_B(V_C-V_B)$

$=-3\times {10}^4\times (V_D-V_A)$

$=-3\times {10}^4\times (2\times {10}^{-3}-2\times {10}^{-3})$

$=-3\times {10}^4\times 0$

$=0\therefore \Delta U_{AC}=Q_{AC}+W_{AC}$

$=Q_{AB}+Q_{BC}+W_{AB}+W_{BC}$

$=600+200+0+0$

$=800J$