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Ideal Gas Equation

An ideal gas ...

Question

An ideal gas follows a process described by $P V^{2} = C$ from $(P_{1}, V_{1}, T_{1})$ to $(P_{2}, V_{2}, T_{2})$ (C is a constant). Then.

A

If

P_{1} > P_{2}

then

T_{2} > T_{1}

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B

If

V_{2} > V_{1}

then

T_{2} < T_{1}

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C

If

V_{2} > V_{1}

then

T_{2} > T_{1}

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D

If

P_{1} > P_{2}

then

V_{2} > V_{2}

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Solution

The correct option is B If $V_{2} > V_{1}$ then $T_{2} < T_{1}$
we know $P V = n R T$
also $P V^{2} = C$
So $\frac{T^{2}}{P} = C_{1}$
$\frac{T_{1}^{2}}{P_{1}} = \frac{T_{2}^{2}}{P_{2}}$
Also $T_{1} V_{1} = T_{2} V_{2}$
So answer B is correct.

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Similar questions

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. Which gas law is summarized with the following equation?

(P_{1} V_{1}) / T_{1} = (P_{2} V_{2}) / T_{2}

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}

p_{2}, V_{2}, T_{2}

under different conditions. The incorrect statement among the following is:

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v_{1}, v_{2} a n d v_{3}

denote the average velocities in the three successive intervals of time

t_{1}, t_{2} a n d t_{3}

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