Question

calculate the kinetic energy of 1 gram mole of gas at NTP. density of gas = 0.178 kg per metre cube at NTP. its molecular weight = 4. density of mercury = 13.6 *1000 kg per metre cube.

Answer 1

For finding kinetic energy of given gas , first we have to find out RMS velocity of gas.
We know the formula of RMS velocity is given by
$\bold{V_{rms}=\sqrt{\frac{3P}{\rho}}}$
Here, P is the pressure , ρ is the density of gas

At NTP , Pressure , P = 1.013 × 10⁵ N/m² and ρ = 0.178 Kg/me
so, $\bold{V_{rms}=\sqrt{\frac{3\times1.013\times10^5}{0.178}}}$
Vrms = 1306.8 m/s

Now, kinetic energy of gas = 1/2MVrms²
Here , M is the molar mass of gas. e.g., M = 4 g/mol = 4 × 10⁻³ Kg/mol
so, Kinetic energy of gas = 1/2 × 4 × 10⁻³ × (1306.8)²
= 3.4 × 10³ Joule

[Note :- given 1 gm mole it means 1 mole of gas . As you know mass of one mole of gas is equal to molecular mass. So, M = 4g/mol]