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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 $2V_0$
A cylinder containing gas at $27\,^oC$ is divided into two parts of equal volume each $100\,^oc$ and at equal pressure by a piston of cross sectional area $10.85\,\, cm^2$. The gas in one part is raised in temperature to $100\,^oC$ while the other maintained at original temperature. The piston and wall are perfect insulators. How far will the piston move during the change in temperature.... $cm$ .
The molecules of a given mass of a gas have a $r.m.s.$ velocity of $200\, m/sec$ at $27°C$ and $1.0 \times {10^5}\,N/{m^2}$ pressure. When the temperature is $127°C$ and pressure is $0.5 \times {10^5}\,N/{m^2}$, the $r.m.s.$ velocity in $m/sec$ will be
If one mole of the polyatomic gas is having two vibrational modes and $\beta$ is the ratio of molar specific heats for polyatomic gas $\left(\beta=\frac{ C _{ P }}{ C _{ v }}\right)$ then the value of $\beta$ is:
The temperature of an ideal gas at atmospheric pressure is $300\,K$ and volume $1\,m^3$. If temperature and volume become double, then pressure will be
One litre of oxygen at a pressure of $1\, atm$ and two litres of nitrogen at a pressure of $0.5\, atm$ are introduced into a vessel of volume $1L$. If there is no change in temperature, the final pressure of the mixture of gas (in $atm$) is