The volume of n moles of a gas at temperature t , and under pressure p is equal to v where p*v = n*r*t. Here, r is a constant equal to 0.082 L*atm/K*mol.

The balloon is filled with 6 moles of nitrogen and it can stretch to a maximum volume of 14 l. The material of the balloon can withstand a maximum pressure of 6 atm. If the maximum temperature of the gas can be T, substituting the given values in the gas law gives:

6*14 = 0.082*6*T

=> T = `(6*14)/(0.082*6)`

=> T `~~` 170.73 K

The gas filled in the balloon can be heated to a maximum temperature of 170.73 K. If the temperature is increased beyond this, the balloon explodes.