A certain amount of an ideal gas is initially at a pressure $${p_1}$$ and temperature $${T_1}$$. First, it undergoes a constant pressure process $$1$$-$$2$$ such that $$T{}_2 = 3{T_1}/4.$$ Then, it undergoes a constant volume process $$2$$-$$3$$ such that $${T_3} = {T_1}/2.$$ The ratio of the final volume to the initial volume of the ideal gas is

A football was inflated to a gauge pressure of $$1$$ bar when the ambient temperature was $${15^ \circ }C$$. When the game started next day, the air temperature at the stadium was $${5^ \circ }C$$.
Assume that the volume of the football remains constant at $$2500c{m^3}$$

The amount of heat lost by the air in the football and the gauge pressure of air in the football at the stadium respectively equal

A football was inflated to a gauge pressure of $$1$$ bar when the ambient temperature was $${15^ \circ }C$$. When the game started next day, the air temperature at the stadium was $${5^ \circ }C$$.
Assume that the volume of the football remains constant at $$2500c{m^3}$$

Gauge pressure of air to which the ball must have been originally inflated so that it would equal $$1$$ bar gauge at the stadium is

Match items from groups, $${\rm I},$$ $${\rm II},$$ $${\rm III},$$ $${\rm IV}$$ and $$V$$