To calculate the increase in volume and diameter of a balloon rising from sea level to the stratosphere, the relationship between volume and temperature can be used, specifically v1/t1 = v2/t2. The initial temperature (t1) is 293K (20°C), while the stratospheric temperature (t2) is assumed to be 270K. Some participants suggest that pressure should also be considered, leading to the equation p1*v1/t1 = p2*v2/t2, but others argue that pressure can be assumed constant since it is not specified in the question. The discussion emphasizes the importance of temperature in determining volume changes in the balloon. Overall, the calculations hinge on the assumptions made about temperature and pressure conditions.