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First Law of Thermodynamics

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

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

T_{1} = T_{2}

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

T_{1} \neq T_{2}

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If the expansion is carried out freely, it is simultaneosly 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
B The work done on 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 The change in internal energy of the gas (i) zero, if it is expanded reversibly with $T_{1} = T_{2}$ , and (ii) negative, if it is expanded reversibly under adiabatic conditions with $T_{1} \neq T_{2}$
D If the expansion is carried out freely, it is simultaneosly both isothermal as well as adiabatic
(A)(B)(C) (i) $Δ U = n C_{v} Δ T = 0$ (isothermal hence $Δ T = 0$ )
(ii) $Δ U = q + w = - v e (q = 0, w < 0)$
$Δ U = n C_{v} Δ T \Rightarrow Δ T < 0$
(D) $q = 0$ (adibatic), $w = 0$ (free expansion)
$Δ U = 0 \Rightarrow Δ T = 0$ (isothermal)

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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)

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) ?

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

. Path

(B + C)

reperesents a reversible adiabatic expansion

(B)

from

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}

. 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} t o P_{2}

V_{2}

T_{1}

What is

q_{r e v}

, for path

(A)

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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)