An ideal gas in a thermally insulated vessel at internal pressure `=p_(1),` volume`=V_1,` and absolute temp`=T_1,` expands irreversibly against zero external pressure, as shown in the below diagram. The final internal pressure volume and absolute temperature of the gas are `p_(2), V_(2), and T_(2),` respectively. For this expansion,

Options

A. `q=0
B. `T _(2) = T _(1)`
C. `p _(2) V _(2) = p _(1) V _(1)`
D. `p _(2) V _(2) ^( gamma) = p _(1) V _(1) ^( gamma)`

Explanation

As the vessel is thermally insulated (so, q = 0). Therefore, `Delta U = 0, Delta T = 0 implies T _(1) = T _(2).` According to combined gas law equation, `( p _(2) V _(2))/( T _(2)) = ( p _(1) V _(1))/( T _(1)) implies p _(2) V _(2) = p _(1) V _(1)`