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 spring 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

B

Explanation

`(P_(1)V_(1))/(T_(1)) = (P_(2)V_(2))/(T_(2))`
If `V_(2) = 2V_(1)` & `T_(2) = 3T_(1)`
`implies P_(2) = (3)/(2)P_(1)`
`DeltaU = (f)/(2)(nRDeltaT) = (3)/(2)(P_(2)V_(2) - P_(1)V_(1))`
`= (3)/(2) xx 2P_(1)V_(1) = 3P_(1)V_(1)`