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First Law of Thermodynamics

An ideal gas ...

Question

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)

A

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

V_{1} t o V_{2}

under adiabatic conditions as compared to that when expanded reversibly from

V_{1} t o V_{2}

under isothermal conditions.

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B

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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C

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

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D

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

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

against constant pressure

p_{1}

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Solution

The correct option is D The work done on the gas is maximum when it is compressed irrversibly from $(p_{2}, V_{2}) t o (p_{1}, V_{1})$ against constant pressure $p_{1}$
(a)

Maximum work is done on the system when compression occur irreversibly and minimum work is done is reversible compression.
(b) AB is isothermal and AC is adiabatic path. Work done is area under the curve. Hence, less work is obtained in adiabatic process than in isothermal
(c) It is incorrect. In adiabatic expansion cooling is observed, hence $Δ U = n C_{v} Δ T < 0$
(d) q = 0 (adiabatic), W = 0 (Free expansion)
Hence, $Δ U = 0, Δ T = 0$ (Isothermal)

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Similar questions

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(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)

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

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Q. An ideal gas is expanded from

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Q. An ideal gas follows a process described by

P V^{2} = C

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

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

(C is a constant). Then.

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) ?

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