Consider a gas with density $\rho $ and $\bar c$ as the root mean square velocity of its molecules contained in a volume. If the system moves as whole with velocity $v,$ then the pressure exerted by the gas is
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A monoatomic ideal gas of two moles is taken through a cyclic process starting from $1$ as shown. $\frac{{{V_2}}}{{{V_1}}} = 2$ and $\frac{{{V_4}}}{{{V_1}}} = 4$ and temperature iast : $1$ is $T_1 = 27\,^oC$. The temperature at $2$ i.e., $T_2$ ...... $K$
Consider two ideal diatomic gases $\mathrm{A}$ and $\mathrm{B}$ at some temperature $T$. Molecules of the gas $A$ are rigid, and have a mass $m$. Molecules of the gas $\mathrm{B}$ have an additional vibrational mode, and have a mass $\frac{\mathrm{m}}{4} .$ The ratio of the specific heats $(\mathrm{C}_{\mathrm{v}}^{\mathrm{A}}$ and $\mathrm{C}_{\mathrm{v}}^{\mathrm{B}})$ of gas $\mathrm{A}$ and $\mathrm{B}$, respectively is
When one mole of monatomic gas is mixed with one mole of a diatomic gas, then the equivalent value of $\gamma$ for the mixture will be (vibration mode neglected)
If three moles of monoatomic gas $\left(\gamma=\frac{5}{3}\right)$ is mixed with two moles of a diatomic gas $\left(\gamma=\frac{7}{5}\right)$, the value of adiabatic exponent $\gamma$ for the mixture is:
In an ideal gas at temperature $T,$ the average force that a molecule applies on the walls of a closed container depends on $T$ as $T^q$ . A good estimate for $q$ is
A diatomic gas follows equation $PV^m =$ constant, during a process. What should be the value of $m$ such that its molar heat capacity during process $= R$
Two vessels having equal volume contains molecular hydrogen at one atmosphere and helium at two atmospheres respectively. If both samples are at the same temperature, the mean velocity of hydrogen molecules is