Two moles of an ideal monoatomic gas are confined within a cylinder by a massless and frictionless spring loaded piston of cross-sectional area `4 xx 10^(-3)m^(2)`. The spring is, initially in its relaxed state. Now the gas is heated by an electric heater, placed inside the cylinder, for some time. During this time, the gas expands and does `50J` of work in moving the piston through a distance `0.10m`. The temperature of the gas increases by `50K`. Calculate the spring constant and the heat supplied by the heater. `P_(atm) = 1 xx 10^(5)N//m^(2)R = 8.314 J//mol-K`

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

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. The force constant of spring is

3 moles of an ideal gas are contained within a cylinder by a frictionless piston and are initially at temperature T . The pressure of the gas remains constant while it is heated and its volume doubles . If R is molar gas constant , the work done by the gas in increasing its volume is

Two moles of an ideal gas is contained in a cylinder fitted with a frictionless movalbe piston, exposed to the atmosphere, at an initial temperature T_(0) . The gas is slowly heated so that its volume becomes fout times the initial value. The wor done by gas is

An ideal monatomic gas is confined in a cylinder by a spring-loaded piston of cross-section 8.0xx10^-3m^2 . Initially the gas is at 300K and occupies a volume of 2.4xx10^-3m^3 and the spring is in its relaxed (unstretched, unompressed) state, fig. The gas is heated by a small electric heater until the piston moves out slowly by 0.1m. Calculate the final temperature of the gas and the heat supplied (in joules) by the heater. The force constant of the spring is 8000 N//m , atmospheric pressure is 1.0xx10^5 Nm^-2 . The cylinder and the piston are thermally insulated. The piston is massless and there is no friction between the piston and the cylinder. Neglect heat loss through lead wires of the heater. The heat capacity of the heater coil is negligible. Assume the spring to be massless.

An ideal monoatomic gas is confined in a horizontal cylinder by a spring loaded piston (as shown in the figure). Initially the gas is at temperature T_1 , pressure P_1 and volume V_1 and the spring is in its relaxed state. The gas is tehn heated very slowly to temperature T_2 ,pressure P_2 and volume V_2 . During this process the piston moves out by a distance x. Ignoring the friction between the piston and the cylinder, the correct statement (s) is (are)

One mole of an ideal gas is contained in a vertical cylinder under a massless piston moving without friction. The piston is slowly raised so that the gas expands isothermally at temperature T_0 = 300 K. Find the amount of work done increasing the volume to eta =2 times. The outside pressure is atmospheric.

Two moles of an ideal monoatomic gas are contained in a vertical cylinder of cross sectional area A as shown in the figure. The piston is frictionless and has a mass m. At a certain instant a heater starts supplying heat to the gas at a constant rate q J//s . Find the steady velocity of the piston under isobaric condition. All the boundaries are thermally insulated.