Option 1 calculates the heat given up as 10000 cal, which is incorrect. Option 2 calculates the heat given up as 11400 cal, which is also incorrect. Option 3 calculates the heat given up as 12400 cal, which is the correct answer. Option 4 calculates the heat given up as 13600 cal, which is incorrect.

When steam at 100°C is condensed and cooled to 20°C, it undergoes a phase change from a gas to a liquid. In order to calculate the heat given up during this process, we need to consider the heat of vaporization and the specific heat capacity of water. The heat of vaporization for water is 540 cal/g, which means that 540 cal are required to convert 1g of steam at 100°C to liquid water at 100°C.

In this scenario, we have 20g of steam, so the heat of vaporization required would be 20g x 540 cal/g = 10800 cal.

Additionally, we need to account for the heat lost when the liquid water cools from 100°C to 20°C. The specific heat capacity of water is 1 cal/g°C, so the heat lost would be 20