Figure shows two flasks connected to each other. The volume of the flask $1$ is twice that of flask $2$. The system is filled with an ideal gas at temperature $100\,K$ and $200\,K$ respectively. If the mass of the gas in $1$ be $m$ then what is the mass of the gas in flask $2$

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, $R=8.31 \,JK ^{-1} mol ^{-1}$ ]

One mole of ideal monoatomic gas $(\gamma \, = \,5/3)$ is mixed with one mole of diatomic gas $(\gamma \, = \,7/5)$ What is $\gamma $ for the mixture ? $\gamma $ denotes the ratio of specific heat at constant pressure, to that at constant volume

At temperature $T, N$ molecules of gas A each having mass $m$ and at the same temperature $2N$ molecules of gas $B$ each having mass $2\,m$ are filled in a container. The mean sqaure velocity of molecules of gas $B$ is $v^2$ and mean square of $x$ component of velocity of molecules of gas$ A$ is $w^2$. The ratio of $w^2/v^2$ is :

A large flask contains air at $27\,^oC$. In order to expel half the mass of air from the flask, the flask should be heated upto what temperature ……. $^oC$