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Concepts Of Physics MCQ Edition [Volume 2]

Exam: Concepts Of Physics MCQ Edition [Volume 2]
Subject: Physics
Chapter: Specific Heat Capacities of Gases

Concepts Of Physics MCQ Edition [Volume 2] · Physics · Specific Heat Capacities of Gases

An ideal gas possessing γ = 1.5 is initially at 300 K with a volume...

An ideal gas possessing

\gamma = 1.5

is initially at

300 \text{ K}

with a volume of

1

litre. It is suddenly compressed to half its original volume. Determine the final temperature of the gas.

Options

A $300\sqrt{2} \text{ K}$
B $600 \text{ K}$
C $150 \text{ K}$
D $150\sqrt{2} \text{ K}$

Correct answer

A. $300\sqrt{2} \text{ K}$

Step-by-step solution

For an adiabatic process, the relation between temperature and volume is

T_1 V_1^{\gamma - 1} = T_2 V_2^{\gamma - 1}

.

Rearranging for the final temperature gives

T_2 = T_1 \left(\dfrac{V_1}{V_2}\right)^{\gamma - 1}

.

Substituting the given values

T_1 = 300 \text{ K}

,

\dfrac{V_1}{V_2} = 2

, and

\gamma = 1.5

:

T_2 = 300 \times (2)^{1.5 - 1} = 300 \times 2^{0.5} = 300\sqrt{2} \text{ K}

.

Using

\sqrt{2} \approx 1.414

, the final temperature is

300 \times 1.414 = 424.2 \text{ K}

.

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