A cylindrical adiabatic container of total volume `2V_(0)` divided into two equal parts by a conducting piston which is free to move as shown in figure. Each part containing identical gas at pressure `P_(0)`. Initially temperature of left and right part is `4T_(0) and T_(0)` respectively. An external force is applied on the piston of area 'A' to keep the piston at rest. The value of external force required when thermal equilibrium is reached is.

A diathermic piston divides adiabatic cylinder of volume V0 into two equal parts as shown in the figure. Both parts contain ideal monoatomic gases. The initial pressure and temperature of gas in left compartment are P0 and T0 while that in right compartment are 2P0 and 2T0. Initially the piston is kept fixed and the system is allowed to acquire a state of thermal equilibrium. The pressure in left compartment after thermal equilibrium is achieved is

A diathermic piston divides adiabatic cylinder of volume V0 into two equal parts as shown in the figure. Both parts contain ideal monoatomic gases. The initial pressure and temperature of gas in left compartment are P0 and T0 while that in right compartment are 2P0 and 2T0. Initially the piston is kept fixed and the system is allowed to acquire a state of thermal equilibrium. The heat that flown from right compartment to left compartment before thermal equilibrium is achieved is

A diathermic piston divides adiabatic cylinder of volume V0 into two equal parts as shown in the figure. Both parts contain ideal monoatomic gases. The initial pressure and temperature of gas in left compartment are P0 and T0 while that in right compartment are 2P0 and 2T0. Initially the piston is kept fixed and the system is allowed to acquire a state of thermal equilibrium. If the pin which was keeping the piston fixed is removed and the piston is allowed to slide slowly such that a state of mechanical equilibrium is achieved. The volume of left compartment when piston is in equilibrium is

In adiabatic container with adiabatic piston contains 4gm N_(2) gas and 0.8 gm He gas are separated by a weakly conducting light partition. Both piston and partition are free ro move. Initial temperature of N_(2) and He gases are '3 T_(0)' and 'T_(0)' respectively. Initially system is at Rest and in equilibrium. Final temperature of the gas is.

In adiabatic container with adiabatic piston contains 4gm N_(2) gas and 0.8 gm He gas are separated by a weakly conducting light partition. Both piston and partition are free ro move. Initial temperature of N_(2) and He gases are '3 T_(0)' and 'T_(0)' respectively. Initially system is at Rest and in equilibrium. Final temperature of the gas is.

An insulting container of volume 2V_(0) is divided in two equal parts by a diathermic (conducting) fixed piston. The left part contains one mole of monoatomic ideal gas whereas right part contains two moles of the same gas. Initial pressue on each side is P_(0) . The system is left for sufficient time so that a steady state is reached. Find (a) the work done by the gas in the left part during the process, (b) initial temperature in the two sides, (c) the final common temperature reached by the gases, (d) the heat given to the gas in the right part and (e) the increase in the internal energy of the gas in the left part.

An insulting container of volume 2V_(0) is divided in two equal parts by a diathermic (conducting) fixed piston. The left part contains one mole of monoatomic ideal gas whereas right part contains two moles of the same gas. Initial pressue on each side is P_(0) . The system is left for sufficient time so that a steady state is reached. Find (a) the work done by the gas in the left part during the process, (b) initial temperature in the two sides, (c) the final common temperature reached by the gases, (d) the heat given to the gas in the right part and (e) the increase in the internal energy of the gas in the left part.

Following figure shows on adiabatic cylindrical container of volume V_(0) divided by an adiabatic smooth piston (area of cross-section = A ) in two equal parts. An ideal gas (C_(p)//C_(y)=lambda) is at pressure P_1 and temperature T_1 in left part and gas at pressure P_2 and temperature T_2 in right part. The piston is slowly displaced and released at a position where it can stay in equilibrium. The final pressure of the two parts will be (Suppose x = displacement of the piston)

Consider the adjacent figure. A piston divides a cylindrical container into two equal parts. The lets part contains 1 mole of helium gas and the right part contains two moles or oxygen gas. The initial temperatures and pressures of the gases in the left chamber are T_(0) and p_(0) and the right chamber are (T_(0))/(2) and p_(0) respectively as shown in the figure. The piston as well as the walls of the container are adiabatic. After removal of the piston, gases mix homoganeously and the final pressure becomes p=(4n)/(13)p_(0) . Find the value of n.

Consider the adjacent figure. A piston divides a cylindrical container into two equal parts. The lets part contains 1 mole of helium gas and the right part contains two moles or oxygen gas. The initial temperatures and pressures of the gases in the left chamber are T_(0) and p_(0) and the right chamber are (T_(0))/(2) and p_(0) respectively as shown in the figure. The piston as well as the walls of the container are adiabatic. After removal of the piston, gases mix homoganeously and the final pressure becomes p=(4n)/(13)p_(0) . Find the value of n.