A small spherical monoatomic ideal gas bubble `(gamma=5//3)` is trapped inside a liquid of density `rho` (see figure). Assume that the bubble does not exchange any heat with the liquid. The bubble contains n moles of gas. The temperature of the gas when the bubble is at the bottom is `T_0`, the height of the liquid is H and the atmospheric pressure `P_0` (Neglect surface tension).
The buyoncy force acting on the gas bubble is (Assume R is the universal gas constant)
A. `rho_l nRgT_0((P_0+rho_lgH)^(2//5))/([P_0+rho_lgy]^(7//5)`
B. `(rho_l nRgT_0)/((P_0+rho_lgH)^(2//5)[P_0rho_lg(H-y)]^(3//5)`
C. `rho_l nRgT_0((P_0+rho_lgH)^(3//5))/([P_0+rho_lgy]^(8//5)`
D. `(rho_l nRgT_0)/((P_0+rho_lgH)^(3//5)[P_0rho_lg(H-y)]^(2//5)`