Question

for a given mass of gas if pressure is reduced to half and the absolute temperature is increased 2 times then the volume would become?

Answer 1

by universal gas equation
p1v1/t1=p2v2/t2
p1*v1/t1=(p1/2)*(v2)/(2*t1)
p1*v1/t1=p1*v2/4*t1
v1=v2/4
v2=4v1

hence the volume becomes 4 times the initial

Answer 2

According to kinetic theory of gases, the gases are made up of molecules.

Since the general gas equation is

$\frac {P_1V_1} {T1}  = \frac {P_2V_2} {T_2}  ;$

The temperature (T) is expressed in degrees absolute (or KELVIN) terms

Here $P_2  =  P_1 / 2  ;$

$T_2  = 2 \times T_1$

So, we get,  

$V_2  = 4 \times V_1  ;$

Hence the effect cause the volume to increase by 4 times.