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 of the gas becomes `Y`. The valve of `P//Y` is

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

An insulated container of gas has two chambers separated by an insulating partition. One of the chambers has volume V_1 and contains ideal gas at pressure P_1 and temperature T_1 .The other chamber has volume V_2 and contains ideal gas at pressure P_2 and temperature T_2 . If the partition is removed without doing any work on the gas, the final equilibrium temperature of the gas in the container will be

Two cylinders A and B of equal capacity are connected to each other via a stopcock. A contains a gas at standard temperature and pressure. B is completely evacuated. The entire system is thermally insulated. The stopcock is suddenly opened. Answer the following: (a) What is the final pressure of the gas in A and B ? (b) What is the change in internal energy of the gas ? (c) What is the change in the temperature of the gas ? (d) Do the intermediate states of the system (before settling to the final equilibrium state) lie on its P-V-T surface ?

Two identical glass bulbs are interconnected by a thin glass tube. A gas is filled in these bulbs at N.T.P. If one bulb is placed in ice and another bulb is placed in hot bath, then the pressure of the gas becomes 1.5 times. The temperature of hot bath will be

A weightless piston divides a thermally insulated cylinder into two parts of volumes V and 3V. 2 moles of an ideal gas at pressure P = 2 atmosphere are confined to the part with volume V =1 litre. The remainder of the cylinder is evacuated. The piston is now released and the gas expands to fill the entire space of the cylinder. The piston is then pressed back to the initial position. Find the increase of internal energy in the process and final temperature of the gas. The ratio of the specific heats of the gas, gamma =1.5 .

A thermally insulated chamber of volume 2V_(0) is divided by a frictionless piston of area S into two equal part A and B . Part A has an ideal gas at pressrue P_(0) and temperature T_(0) and part B is vacuum. A massless spring of force constant K is connected with the piston and the wall of the container as shown. Initially the spring is unstretched. The gas inside chamber A is allowed to expand. Let in equilibrium the spring be compressed by x_(0) . Then

The rectangular box shown in Fig has partition which can slide without friction along the length of the box. Initially each of the two chambers of the box has one mole of a mono-atomic ideal gas (lambda=5//3) at a pressure P_0 , volume V_0 and temperature T_0 . The chamber on the left is slowly heated by an electric heater. The walls of the box and the lead wires of the heater is negligible. The gas in the left chamber expands pushing the partition until the final pressure in both chambers becomes 243P_0//32 . Determine (i) the final temperature of the gas in each chamber and (ii) the work done by the gas in the right chamber.

In Fig., a container is shown to have a movable (without friction) piston on top. The container and the piston are all made of perfectly insulating material allowing no heat transfer between outside and inside the container. The container is divided into two compartments by a rigid partition made of a thermally conducting material that allows slow transfer of heat. the lower compartment of the container is filled with 2 moles of an ideal monoatomic gas at 700 K and the upper compartment is filled with 2 moles of an ideal diatomic gas at 400 K. the heat capacities per mole of an ideal monoatomic gas are C_(upsilon) = (3)/(2) R and C_(P) = (5)/(2) R , and those for an ideal diatomic gas are C_(upsilone) = (5)/(2) R and C_(P) = (7)/(2) R. Now consider the partition to be free to move without friction so that the pressure of gases in both compartments is the same. the total work done by the gases till the time they achieve equilibrium will be

In Fig., a container is shown to have a movable (without friction) piston on top. The container and the piston are all made of perfectly insulating material allowing no heat transfer between outside and inside the container. The container is divided into two compartments by a rigid partition made of a thermally conducting material that allows slow transfer of heat. the lower compartment of the container is filled with 2 moles of an ideal monoatomic gas at 700 K and the upper compartment is filled with 2 moles of an ideal diatomic gas at 400 K. the heat capacities per mole of an ideal monoatomic gas are C_(upsilon) = (3)/(2) R and C_(P) = (5)/(2) R , and those for an ideal diatomic gas are C_(upsilone) = (5)/(2) R and C_(P) = (7)/(2) R. Consider the partition to be rigidly fixed so that it does not move. when equilibrium is achieved, the final temperature of the gases will be

Two thermally insulated vessel 1 and 2 are filled with air at temperature (T_1T_2), volume (V_1V_2) and pressure (P_1P_2) respectively. If the valve joining the two vessels is opened, the temperature inside the vessel at equilibrium will be