A container with insulating walls is divided into two equal parts by a partition fitted with a valve. One part is filled with an ideal gas at a pressure $P$ and temperature $T$, whereas the other part is completely evacuated. If the valve is suddenly opened, the pressure and temperature of the gas will be
A$\frac{P}{2}\,,\,T$
B$\frac{P}{2}\,,\,\frac{T}{2}\,$
C$P, T$
D$P\,,\,\,\frac{T}{2}\,$
AIEEE 2011, Medium
Download our app for free and get started
A$\frac{P}{2}\,,\,T$
a It is the free expansion Internal energy of the gas remains constant, hence
$T_{2}=T$
Using at constant temperature,
$P_{1} V_{1}=P_{2} V_{2}$
$P_{2}=\frac{P}{2}$
Download our app
and get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
A hot air balloon with a payload rises in the air. Assume that the balloon is spherical in shape with diameter of $11.7 \,m$ and the mass of the balloon and the payload (without the hot air inside) is $210 \,kg$. Temperature and pressure of outside air are $27^{\circ} C$ and $1 atm =10^5 \,N / m ^2$, respectively. Molar mass of dry air is $30 \,g$. The temperature of the hot air inside is close to .......... $^{\circ} C$ [The gas constant, $R=8.31 \,JK ^{-1} mol ^{-1}$ ]
Three closed vessels $A, B$ and $C$ are at the same temperature $T$ and contain gases which obey the Maxwellian distribution of velocities. Vessel $A$ contains only ${O_2},\,B$ only ${N_2}$ and $C$ a mixture of equal quantities of ${O_2}$ and ${N_2}$. If the average speed of the ${O_2}$ molecules in vessel A is ${V_1}$, that of the ${N_2}$ molecules in vessel B is ${V_2}$, the average speed of the ${O_2}$ molecules in vessel $C$ is
A cubical box with porous walls containing an equal number of ${O_2}$ and $H_2$ molecules is placed in a large evacuated chamber. The entire system is maintained at constant temperature $T.$ The ratio of ${v_{rms}}$ of ${O_2}$ molecules to that of the ${v_{rms}}$ of $H_2$ molecules, found in the chamber outside the box after a short interval is
Two moles of a monoatomic ideal gas is confined in a container and is heated such that its temperature increases by $10\,^oC$. The approximate change in its internal energy is ..... $J$. $(R = 8.31\, J/mole-K)$
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
The temperature of $5$ moles of a gas which was held at constant volume was changed from ${100^o}C$ to ${120^o}C$. The change in internal energy was found to be $80$ Joules. The total heat capacity of the gas at constant volume will be equal to ...... $J/K$
In a thermally isolated system, two boxes filled with an ideal gas are connected by a valve. When the valve is in closed position, states of the box $1$ and $2$ respectively, are ( $1 \,atm , V, T)$ and $(0.5 \,atm , 4 V, T)$. When the valve is opened, then the final pressure of the system is approximately ............... $atm$