Number of molecules in a volume of 4, cm^{3} | vedclass

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

Question

(C) The pressure $P$ is given by $P = h ho g$,where $h = 2\, cm$,$ho = 13.6\, g/cm^{3}$,and $g = 980\, cm/s^{2}$.$P = 2 	imes 13.6 	imes 980 = 2

Vedclass · Accepted Answer

$4.0 	imes 10^{18}$

Vedclass · Answer

(C) The pressure $P$ is given by $P = h ho g$,where $h = 2\, cm$,$ho = 13.6\, g/cm^{3}$,and $g = 980\, cm/s^{2}$.$P = 2 	imes 13.6 	imes 980 = 26656\, dyne/cm^{2}$.The volume $V = 4\, cm^{3}$.The mean kinetic energy of a monoatomic gas molecule is given by $E = \frac{3}{2} kT = 4 	imes 10^{-14}\, erg$.From the ideal gas law,$PV = NkT$,where $N$ is the number of molecules.We can write $N = \frac{PV}{kT}$.Since $kT = \frac{2}{3} E = \frac{2}{3} 	imes 4 	imes 10^{-14} = \frac{8}{3} 	imes 10^{-14}\, erg$.Substituting the values: $N = \frac{26656 	imes 4}{\frac{8}{3} 	imes 10^{-14}} = \frac{106624 	imes 3}{8 	imes 10^{-14}} = 13328 	imes 3 	imes 10^{14} = 39984 	imes 10^{14} \approx 4.0 	imes 10^{18}$.

Number of molecules in a volume of $4\, cm^{3}$ of a perfect monoatomic gas at some temperature $T$ and at a pressure of $2\, cm$ of mercury is close to $?$
(Given,mean kinetic energy of a molecule (at $T$) is $4 \times 10^{-14}\, erg$,$g=980\, cm/s^{2}$,density of mercury $=13.6\, g/cm^{3}$)

Similar Questions

The ratio of the mean kinetic energy of hydrogen and oxygen at a given temperature is

The time average of the kinetic energy of one molecule of a gas taken over a long period of time:

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?

The internal energy of $4$ moles of a monoatomic gas at a temperature of $77^{\circ} C$ is ($R$ - Universal gas constant). (in $R$)

Consider a gas with density $\rho$ and $\bar{c}$ as the root mean square velocity of its molecules contained in a volume. If the system moves as a whole with velocity $v$,then the pressure exerted by the gas is

Vedclass Test Series

Exam Paper Generator

Online Exam Module

Number of molecules in a volume of $4\, cm^{3}$ of a perfect monoatomic gas at some temperature $T$ and at a pressure of $2\, cm$ of mercury is close to $?$(Given,mean kinetic energy of a molecule (at $T$) is $4 \times 10^{-14}\, erg$,$g=980\, cm/s^{2}$,density of mercury $=13.6\, g/cm^{3}$)