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One mole of an ideal gas passes through a process where pressure and volume obey the relation $P\, = {P_0}\,\left[ {1 - \frac{1}{2}{{\left( {\frac{{{V_0}}}{V}} \right)}^2}} \right]$. Here $P_0$ and $V_0$ are constants. Calculate the change in the temperature of the gas if its volume change from $V_0$ to $2V_0$
If $\alpha$ moles of a monoatomic gas are mixed with $\beta$ moles of a polyatomic gas and mixture behaves like diatomic gas, then [neglect the vibrational mode of freedom]
A spherical bubble inside water has radius $R$. Take the pressure inside the bubble and the water pressure to be $p_0$. The bubble now gets compressed radially in an adiabatic manner so that its radius becomes $(R-a)$. For $a \ll R$ the magnitude of the work done in the process is given by $\left(4 \pi p_0 R a^2\right) X$, where $X$ is a constant and $\gamma=C_p / C_V=41 / 30$. The value of $X$ is. . . . . .
A partition divides a container having insulated walls into two compartments $I$ and $II$. the same gas fills the two compartments. The ratio of the number of molecules in compartments $I$ and $II$ is
An inverted bell lying at the bottom of a lake $47.6\,m$ deep has $50\, cm^3$ of air trapped in it. The bell is brought to the surface of the lake. The volume of the trapped air will be ...... $cm^3$ (atmospheric pressure $= 70\, cm$ of $Hg$ and density of $Hg = 13.6\, g/cm^3$)
The change in volume $V$ with respect to an increase in pressure $P$ has been shown in the figure for a non-ideal gas at four different temperatures ${T_1},\,{T_2},\,{T_3}$ and ${T_4}$. The critical temperature of the gas is