An ideal gas undergoes an expansion from a state with temperature $T_{1}$ and volume $V_{1}$ through three different polytropic processes $A, B a n d C$ as shown in the $P - V$ diagram. If $| ∆ E_{A} |, | ∆ E_{B} | a n d | ∆ E_{C} |$ be the magnitude of changes in internal energy along the three paths respectively, then:

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$| ∆ E_{A} | > | ∆ E_{B} | > | ∆ E_{C} |$ if temperature in every process increases

$| ∆ E_{A} | > | ∆ E_{B} | > | ∆ E_{C} |$ if temperature in every process decreases

$| ∆ E_{A} | < | ∆ E_{B} | < | ∆ E_{C} |$ if temperature in every process decreases

$| ∆ E_{A} | < | ∆ E_{B} | < | ∆ E_{C} |$ if temperature in every process increases

answer is A, C.

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Detailed Solution

Initial state is same for all the three processes (say initial internal energy $= E_{0}$ ).

In the final state,

If $T_{1} < T_{2}, t h e n E_{0} < E_{f}$ for all the three processes and hence

$V_{A} = V_{B} = V_{C} a n d P_{A} > P_{B} > P_{C} \Rightarrow P_{A} V_{A} > P_{B} V_{B} > P_{C} V_{C} . S o f i n a l t e m p e r a t u r e o f A i s m a x i m u m a n d f o r C i t i s m i n i m u m .$

Hence $E_{A} > E_{B} > E_{C} .$

$(E_{0} - E_{A}) < (E_{0} - E_{B}) < (E_{0} - E_{C})$

$| ∆ E_{A} | < | ∆ E_{B} | < | ∆ E_{C} |$

If $T_{1} < T_{2}$ then $E_{0} < E_{f}$ for all the three processes and hence $(E_{A} - E_{0}) > (E_{B} - E_{0}) > (E_{C} - E_{0})$

$| ∆ E_{A} | > | ∆ E_{B} | > | ∆ E_{C} |$

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