SATHEE: Thermodynamics - Result Question 3

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 $δ Q_{1} = 50 J$ and the work done $δ W_{1} = 20 J$ whereas along the path abc the heat absorbed $δ Q_{2} = 36 J$ . The amount of work done along the path $a b c$ is

[NEET Kar. 2013]

(a) $6 J$

(b) $10 J$

(d) $36 J$

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Answer:

Correct Answer: 3. (a)

Solution:

(a) From first law of thermodynamics

$\begin{aligned} Q_{a d c} & = Δ U_{a d c} + W_{a d c} \\ 50 J & = Δ U_{a d c} + 20 J \\ Δ U_{a d c} & = 30 J \\ Q_{a b c} & = Δ U_{a b c} + W_{a b c} \\ W_{a b c} & = Q_{a b c} - Δ U_{a b c} \\ = Q_{a b c} - Δ U_{a d c} \\ = 36 J - 30 J \\ = 6 J \end{aligned}$

$Again, \begin{aligned} Q_{a b c} & = Δ U_{a b c} + W_{a b c} \\ W_{a b c} & = Q_{a b c} - Δ U_{a b c} \end{aligned}$

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Thermodynamics - Result Question 3

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