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 then 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)

Options

A. If`V_(2)=2V_(1)` and`T_(2)=3T_(1),` then the energy stored in the springs is`(1)/(4)P_(1)V_(1)`
B. If` V_(2)=2V_(1)` and `T_(2)=3T_(1)`then the change in internal energy is `3P_(1)V_(1)`
C. If `V_(2)=3V_(1)`and `T_(2)=4T_(1)`then the work done by the gas is `(7)/(3)P_(1)V_(1)`
D. If`V_(2)=3V_(1)`and` T_(2)=4T_(1),`then the heat supplied to the gas is `(17)/(6)P_(1)V_(1)`

Answer

A,B,C