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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 $=13.6\, g / cm ^{3}$)
$310\,J$ of heat is required to raise the temperature of $2\,moles$ of an ideal gas at constant pressure from $25\,^oC$ to $35\,^oC$ . The amount of heat required to raise the temperature of the gas through the same range at constant volume is .... $J$
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 whole with velocity $v,$ then the pressure exerted by the gas is
An ideal gas undergoes a quasi static, reversible process in which its molar heat capacity $C$ remains constant. If during this process the relation of pressure $P$ and volume $V$ is given by $PV^n =$ constant, then n is given by (Here $C_p$ and $C_v$ are molar specific heat at constant pressure and constant volume, respectively) :
$28\,\, gm$ of $N_2$ gas is contained in a flask at a pressure of $10$ atm and at a temperature of $57^o$. It is found that due to leakage in the flask, the pressure is reduced to half and the temperature reduced to $27\,^oC$. The quantity of $N_2$ gas that leaked out is
A vessel contains $14\,g$ of nitrogen gas at a temperature of $27^{\circ}\,C$. The amount of heat to be transferred to the gap to double the r.m.s. speed of its molecules will be $......J$ $\left(\right.$ Take $R =8.32\,J\,mol ^{-1} k ^{-1}$ )
$125\, ml$ of gas $A$ at $0.60$ atmosphere and $150\, ml$ of gas $B$ at $0.80$ atmosphere pressure at same temperature is filled in a vessel of $1$ litre volume. What will be the total pressure of mixture at the same temperature ............... $\mathrm{atmosphere}$