# An ideal gas goes from state A to state B via three different processes as indicated in the P - V diagram:If Q1, Q2, Q3 indicate the heat absorbed by the gas along the three processes and U1, U2, U3 indicate the change in internal energy along the three processes respectively, then: Option 1) Q3 > Q2 > Q1 and U1 = U2 = U3 Option 2) Q1 = Q2 = Q3 and U1 > U2 > U3 Option 3) Q3 > Q2 > Q1 and U1 > U2 > U3   Option 4) Q1 > Q2 > Q3 and U1 = U2 = U3

As we learnt in

Property of internal energy -

U (internal energy) is a state function.

- wherein

i.e. It depends only on initial and final state.

Since change in internal energy is a state function hence

$\Delta U_{1}=\Delta U_{2}=\Delta U_{3}$

work done is $W_{3}< W_{2}< W_{1}$

Since $Q=\Delta U+W$

$\therefore Q_{1}> Q_{2}> Q_{3}$

Correct option is 3.

Option 1)

Q3 > Q2 > Q1 and U1 = U2 = U3

This is incorrect option

Option 2)

Q1 = Q2 = Q3 and U1 > U2 > U3

This is incorrect option

Option 3)

Q3 > Q2 > Q1 and U1 > U2 > U3

This is incorrect option

Option 4)

Q1 > Q2 > Q3 and U= U2 = U3

This is correct option

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