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Three containers of the same volume contain three different gases. The masses of the molecules are ${m_1},\,{m_2}$ and ${m_3}$ and the number of molecules in their respective containers are ${N_1},\,{N_2}$ and ${N_3}$. The gas pressure in the containers are ${P_1},\,{P_2}$ and ${P_3}$ respectively. All the gases are now mixed and put in one of the containers. The pressure $P$ of mixture will be
The temperature of the hydrogen at which the average speed of its molecules is equal to that of oxygen molecules at a temperature of $31\,^oC,$ is ........ $^oC$
One mole of an ideal monatomic gas undergoes a process described by the equation $PV^3 =$ constant. The heat capacity of the gas during this process is
A hot air balloon with a payload rises in the air. Assume that the balloon is spherical in shape with diameter of $11.7 \,m$ and the mass of the balloon and the payload (without the hot air inside) is $210 \,kg$. Temperature and pressure of outside air are $27^{\circ} C$ and $1 atm =10^5 \,N / m ^2$, respectively. Molar mass of dry air is $30 \,g$. The temperature of the hot air inside is close to .......... $^{\circ} C$ [The gas constant, $R=8.31 \,JK ^{-1} mol ^{-1}$ ]
A container is divided into two equal parts $I$ and $II$ by a partition with a small hole of diameter $d$. The two partitions are filled with same ideal gas, but held at temperatures $T_{ I }=150 \,K$ and $T_{ II }=300 \,K$ by connecting to heat reservoirs. Let $\lambda_{1}$ and $\lambda_{1 I}$ be the mean free paths of the gas particles in the two parts, such that $d >> \lambda_{ I }$ and $d >> \lambda_{ II }$. Then, the $\lambda_{ I } / \lambda_{ II }$ is close to
The $rms$ speeds of the molecules of Hydrogen, Oxygen and Carbondioxide at the same temperature are ${V}_{{H}}, {V}_{0}$ and ${V}_{{C}}$ respectively then