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Surface Tension

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Question

A sample of ideal gas undergoes Isothermal expansion in a reversible manner from volume $V_{1}$ to volume $V_{2}$ .
The initial pressure is $P_{1}$ and the final pressure is $P_{2}$ . The same sample is then allowed to undergo reversible expansion under adiabatic conditions from volume $V_{1}$ to $V_{2}$ . The initial pressure being same but final pressure is $P_{2}$ .
which of the following is correct?

A

P_{1} V_{1} = P_{2} V_{2}

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B

P_{1} / P_{2} = V_{1} / V_{2}

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C

P_{1} / P_{2} = P_{1} / P_{3}

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D

P_{1} = P_{2}

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Solution

The correct option is A $P_{1} V_{1} = P_{2} V_{2}$
As we know,
PV = nRT
so at constant temperature,
$P_{1} V_{1} = P_{2} V_{2}$

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Similar questions

Q. A sample of ideal gas undergoes Isothermal expansion in a reversible manner from volume

V_{1}

V_{2}

.
The initial pressure is

P_{1}

and the final pressure is

P_{2}

. The same sample is then allowed to undergo reversible expansion under adiabatic conditions from volume

V_{1}

V_{2}

. The initial pressure being same but final pressure is

P_{2}

.
If true 1 else 0

P_{1} V_{1} = P_{2} V_{2}

For an ideal gas, an illustration of three different paths

A

(B + C)

(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 from

P_{1}

V_{1}

P_{2}, V_{2}

(B + C)

reperesents a reversible adiabatic expansion

(B)

P_{1} V_{1}

T_{1}

P_{3}

V_{2}

T_{2}

followed by reversible heating the gas at constant volume

(C)

P_{3}

V_{2}

T_{2}

P_{2}

V_{2}

T_{1}

(D + E)

represents a reversible expansion at constant pressure

P_{1} (D)

P_{1}

V_{1}

T_{1}

P_{1}

V_{2}

T_{3}

followed by a reversible cooling at constant volume

V_{2} (E)

P_{1}

V_{2}

T_{3}

P_{2}

V_{2}

T_{1}

Δ S

(D + E) ?

Q. For an ideal gas, an illustration of three different paths

A

(B + C)

(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 from

P_{1}

V_{1} t o P_{2}, V_{2}

(B + C)

reperesents a reversible adiabatic expansion

(B)

P_{1} V_{1}

T_{1} t o P_{3}

V_{2}

T_{2}

followed by reversible heating the gas at constant volume (C) from

P_{3}

V_{2}

T_{2} t o P_{2}

V_{2}

T_{1}

(D + E)

represents a reversible expansion at constant pressure

P_{1} (D)

P_{1}

V_{1}

T_{1}

P_{1}

V_{2}

T_{3}

followed by a reversible cooling at constant volume

V_{2} (E)

P_{1}

V_{2}

T_{3} t o P_{2}

V_{2}

T_{1}

q_{r e v}

(A)

?

An ideal gas expands isothermally from a volume $V_{1}$ to $V_{2}$ to and then compressed to original volume $V_{1}$ adiabatically. Initial pressure is $P_{1}$ and final pressure is $P_{3}$ . The total work done is W. Then

n

moles of a perfect gas undergoes a cyclic process

A B C A

(see figure) consisting of the following processes -

A \to B

: Isothermal expansion at temperature

T

so that the volume is doubled from

V_{1}

V_{2}

and pressure changes from

P_{1}

P_{2}

B \to C

: Isobaric compression at pressure

P_{2}

to initial volume

V_{1}

C \to A

: Isochoric change, leading to change of pressure from

P_{2}

P_{1}

.

Total work done in the complete cycle

A B C A

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