Thermodynamics - Result Question 3
3. A system is taken from state $a$ to state $c$ by two paths $a d c$ and $a b c$ as shown in the figure. The internal energy at $a$ is $U_a=10 J$. Along the path $a d c$ the amount of heat absorbed $\delta Q_1=50 J$ and the work done $\delta W_1=20 J$ whereas along the path abc the heat absorbed $\delta Q_2=36 J$. The amount of work done along the path $a b c$ is
[NEET Kar. 2013]
(a) $6 J$
(b) $10 J$
(c) $12 J$
(d) $36 J$
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Answer:
Correct Answer: 3. (a)
Solution:
- (a) From first law of thermodynamics
$ \begin{aligned} Q _{adc} & =\Delta U _{a d c}+W _{a d c} \\ 50 J & =\Delta U _{a d c}+20 J \\ \Delta U _{a d c} & =30 J \\ Q _{a b c} & =\Delta U _{a b c}+W _{a b c} \\ W _{a b c} & =Q _{a b c}-\Delta U _{a b c} \\ & =Q _{a b c}-\Delta U _{a d c} \\ & =36 J-30 J \\ & =6 J \end{aligned} $
$ \text{ Again, } \quad \begin{aligned} Q _{a b c} & =\Delta U _{a b c}+W _{a b c} \\ W _{a b c} & =Q _{a b c}-\Delta U _{a b c} \end{aligned} $
