CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Units and Dimensions

A sample of i...

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 relation is correct $(\begin{matrix} Υ = \frac{C_{P}}{C_{V}} \end{matrix}) ?$

A

P_{1} V_{1} = P_{2} V_{3}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

B

P_{2} V_{1} = P_{3} V_{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

C

P_{1} V_{1}^{Υ} = P_{2} V_{2}^{Υ}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

D

\frac{P_{1}}{P_{2}} = {(\begin{matrix} \frac{V_{2}}{V_{1}} \end{matrix})}^{Υ - 1}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $P_{1} V_{1}^{Υ} = P_{2} V_{2}^{Υ}$
Since it undergoes a reversible adiabatic expansion, we have $P_{1} V_{1}^{γ} = P_{2} V_{2}^{γ}$ .
Hence option C is the right answer.

Suggest Corrections

thumbs-up

0

Similar questions

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)

?

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

Q. An ideal gas expands isothermally from a volume

V_{1}

V_{2}

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

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

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Measurement of Significant Figures

CHEMISTRY

Watch in App

explore_more_icon

Explore more

Units and Dimensions

Standard XII Chemistry

Join BYJU'S Learning Program

CrossIcon