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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Answer:

Correct Answer: 13. (b)

Solution:

  1. 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,

$$ \begin{aligned} \Delta Q _{A D B} & =\Delta W _{A D B}+\left(U _B-U _A\right) \\ \Rightarrow \Delta Q _{A D B} & =10+30 \quad [using Eq. (i)]\\ & =40 J \end{aligned} $$



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