Question

In the Pressure versus Volume graph shown, in the process of going from $a$ to $b,$ $60\text{J}$ of heat is added, and in the process of going from $b$ to $d,$ $20\text{J}$ of heat is added. In the process of going from $a$ to $c$ to $d$, what is the total heat added?

• A. $80\text{J}$
• B. $65\text{J}$
• C. $60\text{J}$
• D. $56\text{J}$

Answer 1

The correct option is B $65\text{J}$

With the help first law of thermodynamics,
For process $a-b-d$
$\Delta Q_{abd}=\Delta U_{abd}+\Delta W_{abd}...\left(i\right)$
For process $a-c-d$
$\Delta Q_{acd}=\Delta U_{acd}+\Delta W_{acd}...\left(i\right)$
(i)- (ii)
$\Delta Q_{abd}-\Delta Q_{acd}=[\Delta W_{abd}-\Delta W_{acd}]+[\Delta U_{abd}-\Delta U_{acd}]$
As internal energy is a point function.
$\Delta U_{abd}=\Delta U_{acd}\Delta Q_{abd}-\Delta Q_{acd}=[\Delta W_{abd}-\Delta W_{acd}]...\left(iii\right)\Delta W_{abd}-\Delta W_{acd}=\text{area under abd}-\text{area under acd}24\text{J}-9\text{J}=15\text{J}$
Putting value in (iii)
$\Delta Q_{abd}-\Delta Q_{acd}=15\Delta Q_{acd}=\Delta Q_{abd}-15=80-15=65\text{J}$
Hence, option (B) is correct.