Occupying 100 cc , an ideal gas is initially at a pressure of 2.5 × 10^5 Pa and a temperature of 300 K . It is adiabatically compressed to half its original volume. Determine the final temperature of the gas. Take γ =

Question

Quantrex Academy · Accepted Answer

Correct answer: B. 424 K

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

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

Given

T_1 = 300 \text{ K}

,

V_1 = V

,

V_2 = \dfrac{V}{2}

, and

\gamma = 1.5

.

Substituting the values in the equation:

300 \times V^{1.5 - 1} = T_2 \times \left(\dfrac{V}{2}\right)^{1.5 - 1}

300 \times V^{0.5} = T_2 \times \dfrac{V^{0.5}}{2^{0.5}}

T_2 = 300 \times \sqrt{2}

T_2 = 300 \times 1.414 = 424.2 \text{ K}

The final temperature of the gas is approximately

424 \text{ K}

.

Occupying 100 cc , an ideal gas is initially at a pressure of 2.5 ×...

Options

Correct answer

Step-by-step solution

More from Specific Heat Capacities of Gases