Question

The V cc volume of gas having `γ = 5/2` is suddenly compressed to `(V/4)` cc. The initial pressure of the gas is p. The final pressure of the gas will be ______.

Options

• 32 p

• 16 p

• `p/32`

• `p/16`

Answer 1

The V cc volume of gas having `γ = 5/2` is suddenly compressed to `(V/4)` cc. The initial pressure of the gas is p. The final pressure of the gas will be 32 p.

Explanation:

For adiabatic process,

`p_2V_2^gamma = p_1V_1^gamma`

⇒ `p_2 = p_1(V_1/V_2)^gamma`

Here, `V_1 = V, V_2 = V/4, p_1 = p` and `gamma = 5/2`

⇒ `p_2 = p(V/(V/4))^{5"/"2} = (4)^{5"/"2}p = 2^5p = 32 p`