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Question

A sample of ideal gas goes from state A to state B for as shown in the graph. Let W be the work done by gas and ΔU be the change in internal energy along the path AB. Identify the correct statement.


A
Both W and ΔU are positive
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B
W=0 and ΔU is negative
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C
W is negative and ΔU is positive
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D
Both W and ΔU are negative
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Solution

The correct option is C W is negative and ΔU is positive
Here Volume V is on vertical axis, however the work done by gas W is obtained by area under PV curve.


In part I,
Volume increases from A to O. Thus, work done by gas is +ve.

However, for Part II,
Volume decreases from O to B and a larger area under the curve suggest a higher ve work.

Hence, for process AB,
Wnet<0

From A to B

At constant volume, pressure increases So from ideal gas equation, temperature will also increase.

Since, TA<TB, So, ΔU>0.

Hence, option (c) is correct.

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