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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:

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}

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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

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C

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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D

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

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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
D If the expansion is carried out freely, it is simultaneously both isothermal as well as adiabatic
Case of expanding thus $\to V_{2} > V_{1}$
Work done in case of isothermal :
$W_{r e v} = - n R T l n \frac{V_{f i n a l}}{V_{I n t i a l}}$
$W_{i r r} = - p_{E x t} (V_{F i n a l} - V_{I n t i a l})$

Option -A:
The work done on the gas is positive because the gas is compressed; the surroundings do positive work on the gas. Note that the work done on the gas is greater for the irreversible process
w_irr > w_rev

Option-B: $| W_{i s o t h e r m} > W_{a d i a b a t i c} |$

Option -C:

(I) zero
$T_{1} = T_{2} = t e m p c o n s t a n t, i . e, △ T = 0$
$△ E = n C_{v} △ T = 0$
(ii) postive
$T_{1} \neq T_{2}$ during adiabatic expansion internal energy decreases .

Option -D:

$P_{e x t = 0}$ , isothermal, $△ E = 0 : q = 0$
$w = 0 a d i a b a t i c$
$q = 0$
$△ E = 0$

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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)

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. 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}

.
which of the following is correct?

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

V_{1}

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w_{1}

, if the process is purely isothermal,

w_{2}

if purely isobaric and

w_{3}

if purely adiabatic, then:

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