Question

In a cubical box of volume V, there are N molecules of a gas moving randomly. If m is mass of each molecule and v² is the mean square of x component of the velocity of molecules, then the pressure of the gas is ______.

Options

• P = `1/3 (mNv^2)/V`

• P = `(mNv^2)/V`

• P = `1/3mNv^2`

• P = mNv²

Answer 1

In a cubical box of volume V, there are N molecules of a gas moving randomly. If m is mass of each molecule and v² is the mean square of x component of the velocity of molecules, then the pressure of the gas is `bbunderline(P = (mNv^2)/V)`.

Explanation:

P = `(nRT)/V = (mN)/m (RT)/V`

Now `3V_x^2 = V_{rms}^2 ⇒ (3RT)/M`

= `V_x^2 = (RT)/M = V^2`

m = mass of molecule

So P = `(mNV^2)/V`

N = number of molecules.