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

In an adiabatic change, the pressure $P$ and temperature $T$ of a diatomic gas are related by the relation $P \propto {T^C}$, where $C$ equal to

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

If $V_{rms}$ for $O_2$ molecules is $V$ at temperature $T\, K$. Then $V_{rms}$ for oxygen atoms at temperature $2T$ will be

At $0\,^oC$ , the value of the density of fixed mass of an ideal gas divided by its pressure is $x$ . At $100\,^oC$ , this value will be