A balloon contains $1500 \,m^3$ of helium at $27^\circ C$ and $4$ atmospheric pressure. The value of helium at $ - \,3^\circ C$ temperature and $2$ atmospheric pressure will be ...... $m^3$
A$1500$
B$1700$
C$1900$
D$2700$
Medium
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D$2700$
d $\frac{{{P_1}{V_1}}}{{{T_1}}} = \frac{{{P_2}{V_2}}}{{{T_2}}}$
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The molecular weights of $O_2$ and $N_2$ are $32$ and $28$ respectively. At $15°C,$ the pressure of $1 \,gm$ $O_2$ will be the same as that of $1 \,gm$ $N_2$ in the same bottle at the temperature ...... $^oC$
If one mole of the polyatomic gas is having two vibrational modes and $\beta$ is the ratio of molar specific heats for polyatomic gas $\left(\beta=\frac{ C _{ P }}{ C _{ v }}\right)$ then the value of $\beta$ is:
Calculate the value of mean free path $(\lambda)$ for oxygen molecules at temperature $27^{\circ}\, C$ and pressure $1.01 \times 10^{5} \,Pa$. Assume the molecular diameter $0.3 \,nm$ and the gas is ideal. $\left( k =1.38 \times 10^{-23}\, J\,K ^{-1}\right)$ (in $nm$)
Two vessels separately contain two ideal gases $A$ and $B$ at the same temperature, the pressure of $A$ being twice that of $B.$ Under such conditions, the density of $A$ is found to be $1.5$ times the density of $B.$ The ratio of molecular weight of $A$ and $B$ is
The temperature, at which the root mean square velocity of hydrogen molecules equals their escape velocity from the earth is closest to : [Boltzmans Constant $k_B = 1.38\times10^{-23}\, J / K$ Avogadro number $N_A = 6.02\times10^{26}\, / kg$ Radius of Earth $: 6.4\times10^6\, m$ Gravitation acceleration on Earth $= 10\, ms^{-2}$]
$Assertion :$ The ratio of $\frac{C_p}{C_v}$ for an ideal diatomic gas is less than that for an ideal monoatomic gas (where $C_p$ and $C_v$ have usual meaning).
$Reason :$ The atoms of a monoatomic gas have less degrees of freedom as compared to molecules of the diatomic gas.
When unit mass of water boils to become steam at $100\,^0C$, it absorbs $Q$ amount of heat. The densities of water and steam at $100\,^0C$ are $\rho_1$ and $\rho_2$ respectively and the atmospheric pressure is $p_0$. The increase in internal energy of the water is