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Ideal Gas Equation

Which is corr...

Question

Which is correct about Ideal gas?

A

$\frac{V_{1}}{T_{1}} = \frac{V_{2}}{T_{2}}$

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B

$P_{1} V_{1} = P_{2} V_{2}$

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C

$\frac{P_{1} V_{1}}{T_{1}} = \frac{P_{1} V_{2}}{T_{2}}$

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D

$V_{1} T_{1} = V_{2} T_{2}$

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Solution

The correct options are
A
$\frac{V_{1}}{T_{1}} = \frac{V_{2}}{T_{2}}$

B
$P_{1} V_{1} = P_{2} V_{2}$

C
$\frac{P_{1} V_{1}}{T_{1}} = \frac{P_{1} V_{2}}{T_{2}}$

Boyle's Law establish relationship between Pressure and Volume-

$P_{1} V_{1} = P_{2} V_{2}$

Charle's Law establish relation between Volume nad Temperature -

$\frac{V_{1}}{T_{1}} = \frac{V_{2}}{T_{2}}$

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Q. An ideal gas is expanded from

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

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\frac{V_{1}}{T_{1}} = \frac{V_{2}}{T_{2}}

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

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V_{1}

P_{2}, V_{2}

(B + C)

reperesents a reversible adiabatic expansion

(B)

P_{1} V_{1}

T_{1}

P_{3}

V_{2}

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followed by reversible heating the gas at constant volume

(C)

P_{3}

V_{2}

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P_{2}

V_{2}

T_{1}

(D + E)

represents a reversible expansion at constant pressure

P_{1} (D)

P_{1}

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T_{1}

P_{1}

V_{2}

T_{3}

followed by a reversible cooling at constant volume

V_{2} (E)

P_{1}

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Δ S

(D + E) ?

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