Heat and Thermodynamics 5 Question 12
13. A gas can be taken from $A$ to $B$ via two different processes $A C B$ and $A D B$.
(2019 Main, 9 Jan I)
When path $A C B$ is used $60 J$ of heat flows into the system and $30 J$ of work is done by the system. If path $A D B$ is used work done by the system is $10 J$ the heat flow into the system in path $A D B$ is
(a) $80 J$
(b) $40 J$
(c) $100 J$
(d) $20 J$
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Solution:
- For the $A B C$ as shown in the figure below,
According to the first law of thermodynamics, heat supplied, $\Delta Q=$ work done $(\Delta W)+$ internal energy $(\Delta U)$
$\Rightarrow \quad \Delta Q _{C B}=\Delta W _{A C B}+\left(U _B-U _A\right)$
[where, $\Delta U=U _B-U _A$ ]
Substituting the given values,
$$ U _B-U _A=60-30=30 J $$
Similarly for the $A D B$ as shown in the figure below,
$$ \begin{aligned} \Delta Q _{A D B} & =\Delta W _{A D B}+\left(U _B-U _A\right) \\ \Rightarrow \Delta Q _{A D B} & =10+30 \\ & =40 J \end{aligned} $$
[using Eq. (i)]
