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For an ideal gas, an illustration of thr...

For an ideal gas, an illustration of three different paths `A(B+C)` and `(D+E)` from an initial state `P_(1), V_(1), T_(1)` to a final state `P_(2), V_(2),T_(1)` is shown in the given figure.

Path `A` represents a reversible isothermal expansion form `P_(1),V_(1)` to `P_(2),V_(2)`, Path `(B+C)` represents a reversible adiabatic expansion `(B)` from `P_(1),V_(1),T_(1)to P_(3),V_(2),T_(2)` followed by reversible heating the gas at constant volume `(C)`from `P_(3),V_(2),T_(2)` to `P_(2),V_(2),T_(1)`. Path `(D+E)` represents a reversible expansion at constant pressure `P_(1)(D)` from `P_(1),V_(1),T_(1)` to `P_(1),V_(2),T_(3)` followed by a reversible cooling at constant volume `V_(2)(E)` from `P_(1),V_(2),T_(3) to P_(2),V_(2),T_(1)`.
What is `DeltaS` for path `(D +E)`?

A

Both the statements are true, and Statement 2 is the correct explanation for Statement 1.

B

Both the Statements are true, but Statement 2 is not the correct explanation for Statement 1.

C

Statement 1 is true and Statement 2 is false.

D

Statement 1 is false and Statement 2 is true.

Text Solution

Verified by Experts

The correct Answer is:
d
Direction ratios of the given lines are `(-3, 1, -1) and (1, 2, -1)`. Hence, the lines are perpendicular as `(-3)(1)+ (1)(2)+ (-1)(-1)=0`.
Also lines are coplanar as
`" "|{:(0-2,,1-3,,-1+(13//7)),(-3,,1,,-1),(1,,2,,-1):}|=0`
But Statement 2 is not enough reason for the shortest distance to be zero, as two skew lines can also be perpendicular.
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