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$3\,moles$ of an ideal gas at a temperature of $27^{\circ}\,C$ are mixed with $2\,moles$ of an ideal gas at a temperature $227^{\circ}\,C$, determine the equilibrium temperature (${}^o C$) of the mixture, assuming no loss of energy.
When a gas filled in a closed vessel is heated by raising the temperature by $1^{\circ} C$, its pressure increase by $0.4 \%$. The initial temperature of the gas is ..........$K$
$C{O_2}(O - C - O)$ is a triatomic gas. Mean kinetic energy of one gram gas will be (If $N-$Avogadro's number, $k-$Boltzmann's constant and molecular weight of $C{O_2} = 44$)
A mixture of $2$ moles of helium gas (atomic mass $=4 \ amu$ ), and $1$ mole of argon gas (atomic mass $=40 \ amu$ ) is kept at $300 \ K$ in a container. The ratio of the rms speeds $\left(\frac{\left. v _{ mms } \text { (helium }\right)}{ v _{\text {rms }} \text { (argon) }}\right)$ is :
A cylinder of $5$ litre capacity, filled with air at $N.T.P.$ is connected with another evacuated cylinder of $30$ litres of capacity. The resultant air pressure in both the cylinders will be ...... $cm$ of $Hg$