Melting of ice is an adiabatic or an isothermal process ?

Does the internal energy of an ideal gas change in an adiabatic process ?

If $\gamma = 2.5$ and volume is equal to $\frac{1}{8}$ times to the initial volume then pressure $P' $ is equal to (Initial pressure $= P$)

A cylinder with a movable piston contains $3\,moles$ of hydrogen at standard temperature and pressure. The walls of the cylinder are made of a heat insulator, and the piston is insulated by having a pile of sand on it. By what factor does the pressure of the gas increases if the gas is compressed to half its original volume? 

A cycle followed by an engine (made of one mole of an ideal gas in a cylinder with a piston) is shown in figure. Find heat exchanged by the engine, with the surroundings for each section of the cycle.${C_v} = \frac{3}{2}R$

$(a)$ $A$ to $B$ : constant volume

$(b)$ $B$ to $C$ : constant pressure

$(c)$ $C$ to $D$ : adiabatic

$(d)$ $D$ to $A$ : constant pressure

Consider a spherical shell of radius $R$ at temperature $T$. The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume$E=$ $\frac{U}{V} \propto {T^4}$ and pressure $P = \frac{1}{3}\left( {\frac{U}{V}} \right)$ If the shell now undergoes an adiabatic expansion the relation between $T$ and $R$ is