Answer
$k = 5$
New pressure P, when volume reduced to 80 litres = 19.375 atm
Work Step by Step
Volume V varies directly proportional with temperature T and inversely to pressure P
$V = k\frac{T}{P}$
given V = 100 ltr, T=300K, and P = 15 atm
=> $100 = k\frac{300}{15}$
=> k = 5
Now, To find P, when V becomes 80litres and T = 310K
$80 = k\frac{310}{P}$
=>$P = \frac{5*310}{80} = 19.375\ atm$
