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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, $R=8.31 \,JK ^{-1} mol ^{-1}$ ]
$0.056 \,kg$ of Nitrogen is enclosed in a vessel at a temperature of $127\,^{\circ} C$. The amount of heat required to double the speed of its molecules is k cal. (Take $R =2$ $cal \,mole$ $^{-1} K ^{-1}$ )
$14 \,g$ of $CO$ at $27^{\circ} C$ is mixed with $16 g$ of $O _2$ at $47^{\circ} C$. The temperature of mixture is .......... $^{\circ} C$ (vibration mode neglected)
To what temperature should the hydrogen at room temperature $(27°C)$ be heated at constant pressure so that the $R.M.S.$ velocity of its molecules becomes double of its previous value ....... $^oC$