Assuming the expression for the pressure exer | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The pressure $P$ exerted by an ideal gas is given by the kinetic theory of gases as:$P = \frac{1}{3} \rho v_{rms}^2$where $\rho = \frac{M}{V}$ is

Vedclass · Accepted Answer

$(2/3)$ of kinetic energy per unit volume of a gas.

Vedclass · Answer

(B) The pressure $P$ exerted by an ideal gas is given by the kinetic theory of gases as:$P = \frac{1}{3} \rho v_{rms}^2$where $\rho = \frac{M}{V}$ is the density of the gas and $v_{rms}$ is the root-mean-square speed.Substituting $\rho$ in the equation:$P = \frac{1}{3} \left( \frac{M}{V} \right) v_{rms}^2$Multiply and divide the right side by $2$:$P = \frac{2}{3} \left( \frac{1}{2} \frac{M}{V} v_{rms}^2 \right)$Since the total kinetic energy $K.E. = \frac{1}{2} M v_{rms}^2$,the kinetic energy per unit volume is $u = \frac{K.E.}{V} = \frac{1}{2} \rho v_{rms}^2$.Therefore,$P = \frac{2}{3} u$.

Assuming the expression for the pressure exerted by the gas,it can be shown that pressure is

Similar Questions

$A$ flask contains Hydrogen and Argon in the ratio $2:1$ by mass. The temperature of the mixture is $30^{\circ} C$. The ratio of average kinetic energy per molecule of the two gases $(K_{\text{argon}} / K_{\text{hydrogen}})$ is: (Given: Atomic weight of $Ar = 39.9$)

The pressure of a gas is $6 \times 10^4 \ N/m^2$. What will be the kinetic energy per unit volume of the gas molecules?

Vessel $A$ is filled with hydrogen while vessel $B,$ whose volume is twice that of $A,$ is filled with the same mass of oxygen at the same temperature. The ratio of the mean kinetic energies of hydrogen and oxygen is

The average translational kinetic energy of nitrogen (molar mass $28$) molecules at a particular temperature is $0.042 \ eV$. The translational kinetic energy of oxygen molecules (molar mass $32$) in $eV$ at double the temperature is:

At constant volume,the pressure of a gas is directly proportional to:

Vedclass Test Series

Exam Paper Generator

Online Exam Module