A resistance coil, connected to an external battery is placed inside an adiabatic cylinder filled with frictionless piston of mass `m` and containing an ideal gas. A current `i` flows through the coil, which has resistance `R`. The speed with which the piston must move in order to keep the temperature of the gas constant will be

A resistance coil of resistance r connected to an external battery, is placed inside an adiabatic cylinder fitted with a frictionless platon of mass m and same area A. Initially cylinder contains one mole of ideal gas he. A current through the coil such that temperature of gas varies as T=T_(0)+"at"+"bt"^(2), keeping pressure constant with time t. Atosphere pressure above piston is P_(0) . Find (a) Current l flowing through the coil as function of time and (b) Speed of piston as function of time.

A Perfect gas is enclosed in a vertical cylinder filled with a piston of mass m. The gas is heated by passing constant current I through a heating coil of resistance R placed inside the cylinder. At what speed v must the piston move upward in order that temperature of the gas may remain unchanges? Assume ideal insulating walls and piston and there is no fusion.

A cylinder containing an ideal gas is in vertical position and has a piston of mass M that is able to move up or down without friction (figure). If the temperature is increased

A vertical cylinder of cross-section area A contains one mole of an ideal mono-atmic gas under a piston of mass M At a certain instant a heater which supplies heat at the rate q J//s is switched ON under the piston. The velocity with which the piston moves upward under the condition that pressure of gas remains constant is [Assume on heat transfer through walls of cylinder]

Two mole of an ideal monatomic gas are confined within a cylinder by a mass less spring loaded with a frictionless piston of negligible mass and crossectional area 4xx10^(-3)m^(2) . The gas is heated by a heater for some time. During this time the gas expands and does 50J of work in moving the piston through a distance of 0.01 m. The temperature of gas increases by 50 k. The force constant of spring is

Two mole of an ideal monatomic gas are confined within a cylinder by a mass less spring loaded with a frictionless piston of negligible mass and crossectional area 4xx10^(-3)m^(2) . The gas is heated by a heater for some time. During this time the gas expands and does 50J of work in moving the piston through a distance of 0.01 m. The temperature of gas increases by 50 k. Change in internal energy of the gas is

Two mole of an ideal monatomic gas are confined within a cylinder by a mass less spring loaded with a frictionless piston of negligible mass and crossectional area 4xx10^(-3)m^(2) . The gas is heated by a heater for some time. During this time the gas expands and does 50J of work in moving the piston through a distance of 0.01 m. The temperature of gas increases by 50 k. Heat supplied by heater during this process is

(i) A conducting piston divides a closed thermally insulated cylinder into two equal parts. The piston can slide inside the cylinder without friction. The two parts of the cylinder contain equal number of moles of an ideal gas at temperature T_(0) . An external agent slowly moves the piston so as to increase the volume of one part and decrease that of the other. Write the gas temperature as a function of ratio (beta) of the volumes of the larger and the smaller parts. The adiabatic exponent of the gas is gamma . (ii) In a closed container of volume V there is a mixture of oxygen and helium gases. The total mass of gas in the container is m gram. When Q amount of heat is added to the gas mixture its temperature rises by Delta T . Calculate change in pressure of the gas.