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Ideal Gas Equation

For an ideal ...

Question

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 $P_{1}$ , $V_{1}$ to $P_{2}, V_{2}$ . Path $(B + C)$ reperesents a reversible adiabatic expansion $(B)$ from $P_{1} V_{1}$ , $T_{1}$ to $P_{3}$ , $V_{2}$ , $T_{2}$ followed by reversible heating the gas at constant volume $(C)$ from $P_{3}$ , $V_{2}$ , $T_{2}$ to $P_{2}$ , $V_{2}$ , $T_{1}$ . Path $(D + E)$ represents a reversible expansion at constant pressure $P_{1} (D)$ from $P_{1}$ , $V_{1}$ , $T_{1}$ to $P_{1}$ , $V_{2}$ , $T_{3}$ followed by a reversible cooling at constant volume $V_{2} (E)$ from $P_{1}$ , $V_{2}$ , $T_{3}$ to $P_{2}$ , $V_{2}$ , $T_{1}$ . What is $Δ S$ for path $(D + E) ?$

A

n R l n \frac{V_{2}}{V_{1}}

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B

+ P (V_{2} - V_{1})

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C

- P (V_{2} - V_{1})

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D

- n R l n \frac{V_{2}}{V_{1}}

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Solution

The correct option is A $n R l n \frac{V_{2}}{V_{1}}$
Path $(D + E)$ represents a reversible expansion at constant pressure $P_{1} (D)$ from $(P_{1}, V_{1}, T_{1})$ to $(P_{1}, V_{2}, T_{3})$
$△ S = n R l n (\frac{V_{2}}{V_{1}})$ (from the formula of change in entropy)

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Similar questions

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}

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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)

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followed by reversible heating the gas at constant volume (C) from

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T_{2} t o P_{2}

V_{2}

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P_{1}

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T_{1}

P_{1}

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T_{3}

followed by a reversible cooling at constant volume

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