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 strored in the spring is `1/4 P _(1)V_(1)`
B. If `V _(2) =2V_(1) and T_(2) =3T,` then the change in internal energy is `3 P _(1) V _(1)`
C. If `V _(2) =3V_(1) and T_(2) =4T,` 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),` the heat supplied to the gas is `(17)/(6) P _(1) V _(1)`

Answer

A, B