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Identification of Different Process

An ideal gas ...

Question

An ideal gas is expanded from $(p_{1}, V_{1}, T_{1})$ to $(p_{2}, V_{2}, T_{2})$ under different conditions. The correct statement(s) among the following is(are):

The work done on the gas is maximum when it is compressed irreversibly from

(p_{2}, V_{2})

(p_{1}, V_{1})

against constant pressure

p_{1}

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The work done by the gas is less when it is expanded reversibly from

V_{1}

V_{2}

under adiabatic conditions as compared to that when expanded reversibly from

V_{1}

V_{2}

under isothermal conditions.

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If the expansion is carried out freely, it is simultaneously both is isothermal as well as adiabatic.

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The change in internal energy of the gas is (i) zero, if it is expanded reversibly with

T_{1} = T_{2}

, and (ii) positive, if it is expanded reversibly under adiabatic conditions with

T_{1} \neq T_{2}

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Solution

The correct options are
A The work done on the gas is maximum when it is compressed irreversibly from $(p_{2}, V_{2})$ to $(p_{1}, V_{1})$ against constant pressure $p_{1}$ .
B The work done by the gas is less when it is expanded reversibly from $V_{1}$ to $V_{2}$ under adiabatic conditions as compared to that when expanded reversibly from $V_{1}$ to $V_{2}$ under isothermal conditions.
C If the expansion is carried out freely, it is simultaneously both is isothermal as well as adiabatic.
(A) $ω = - P e x t Δ V$
Work done on gas when compressed
$ω =$ is positive
$∴$ equation becomes
$ω = P e x t Δ V$

(B) under adiabatic conditions
$ω = \frac{(P_{2} V_{2} - P_{1} V_{1})}{(γ - 1)}$
since equation $V_{2} > V_{1}$
$∴ ω = + v e$ (work done on system)
for reversibly condition (Isothermal)
$ω = - n R T l n \frac{V_{2}}{V_{1}}$
$= V_{2} > V_{1}$
$ω = - v e$ (work done on system)
$ω = - v e$ (for adiabatic reversibly work done by gas)
$ω = + v e$ (for isothermal reversibly work done by gas)

(C) As free expansion in there (irreserible)
$∴ P e x t = 0$
$ω = (- P e x t \times Δ V) = 0$ (Isothermal irreversible process)
In adiabatic $Δ U = - v e$
$Δ U = q + ω$
$- = 0 + ω$
$ω = -$ negative
similarly, $Δ G = Δ H - T Δ s$

gas expand $∴ Δ s = + v e$
$Δ G = Δ H - V e$
$= Δ V + p Δ V - v e$
$= q + w + p Δ c - v e$
$= o + w + w - v e$
$= - v e + (- v e) - v e$
$Δ G = - v e$
$∴$ It is spontaneous process
$∴$ both take place simultaneously

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Similar questions

Q. An ideal gas is expanded from

(p_{1}, V_{1}, T_{1})

(p_{2}, V_{2}, T_{2})

under different conditions. The correct statement(s) among the following is/are:

Q. An ideal gas is expanded from

(p_{1}, V_{1}, T_{1}) t o (p_{2}, V_{2}, T_{2})

under different conditions. The correct statement(s) among the following is (are)

Q. Starting with the same initial conditions, one mole of an ideal monoatomic gas expands reversibly from volume

V_{1}

V_{2}

in two different ways. The work done by gas is

w_{1}

, if the process is purely isothermal,

w_{2}

if purely isobaric and

w_{3}

if purely adiabatic, then:

Q. 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}

V_{2}

. The initial pressure being same but final pressure is

P_{2}

.
which of the following is correct?

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 from

P_{1}

V_{1}

P_{2}, V_{2}

. Path

(B + C)

reperesents a reversible adiabatic expansion

(B)

from

P_{1} V_{1}

T_{1}

P_{3}

V_{2}

T_{2}

followed by reversible heating the gas at constant volume

(C)

from

P_{3}

V_{2}

T_{2}

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}

P_{1}

V_{2}

T_{3}

followed by a reversible cooling at constant volume

V_{2} (E)

from

P_{1}

V_{2}

T_{3}

P_{2}

V_{2}

T_{1}

. What is

Δ S

for path

(D + E) ?

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An ideal gas is expanded from (p1,V1,T1) to (p2,V2,T2) under different conditions. The correct statement(s) among the following is(are):

An ideal gas is expanded from $(p_{1}, V_{1}, T_{1})$ to $(p_{2}, V_{2}, T_{2})$ under different conditions. The correct statement(s) among the following is(are):