$1\, mole$ of ideal monoatomic gas $\left( {\gamma  = 5/3} \right)$ is mixed with $1\, mole$ of diatomic gas $\left( {\gamma  = 7/5} \right)$. What is $\gamma $ for the mixture ? $\gamma $ denotes the ratio of specific heat at constant pressure, to that at constant volume

A gaseous mixture consists of $16\  g$ of helium and $16\  g$ of oxygen. The ratio $\frac{{{C_p}}}{{{C_v}}}$ of the mixture is

A vessel contains $14 \,gm \,(7 $ moles) of hydrogen and $96\, gm$ ($9$ moles) of oxygen at $STP.$ Chemical reaction is induced by passing electric spark in the vessel till one of the gases is consumed. The temperature is brought back to it's starting value $273 K.$ The pressure in the vessel is …… $atm$

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 $2$

An ideal gas is trapped inside a test tube of cross-sectional area $20 \times 10^{-6} \,\,m^2$ as shown in the figure. The gas occupies a height $L_1$ at the bottom of the tube and is separated from air at atmospheric pressure by a mercury column of mass $0.002\,\, kg$. If the tube is quickly turned isothermally, upside down so that $L_2$ mercury column encloses the gas from below. The gas now occupies height $L_1$ in the tube. The ratio $L_1$ is [Take atmospheric pressure $= 10^5 Nm^{-2}]$