Thermodynamics - Result Question 4

4. An ideal gas goes from state $A$ to state $B$ via three different processes as indicated in the $P-V$ diagram:

[2012M]

If $Q_1, Q_2, Q_3$ indicate the heat a absorbed by the gas along the three processes and $\Delta U_1, \Delta U_2$, $\Delta U_3$ indicate the change in internal energy along the three processes respectively, then

(a) $Q_1>Q_2>Q_3$ and $\Delta U_1=\Delta U_2=\Delta U_3$

(b) $Q_3>Q_2>Q_1$ and $\Delta U_1=\Delta U_2=\Delta U_3$

(c) $Q_1=Q_2=Q_3$ and $\Delta U_1>\Delta U_2>\Delta U_3$

(d) $Q_3>Q_2>Q_1$ and $\Delta U_1>\Delta U_2>\Delta U_3$

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Answer:

Correct Answer: 4. (a)

Solution:

  1. (a) Initial and final condition is same for all process

$\Delta U_1=\Delta U_2=\Delta U_3$

from first law of thermodynamics

$\Delta Q=\Delta U+\Delta W$

Work done

$\Delta W_1>\Delta W_2>\Delta W_3$ (Area of P.V. graph)

So $\Delta Q_1>\Delta Q_2>\Delta Q_3$