Final answer:
The total heat lost by steam as it condenses and cools to 50°C is equal to the heat gained by the container and water, which is 6300 cal. This is based on calorimetry and the conservation of energy in an isolated system. Option A is correct.
Step-by-step explanation:
The question asks about the total heat lost by steam as it condenses and cools to 50°C. To calculate this, one must consider the heat released during the phase change from steam to water, as well as the subsequent cooling of the water from 100°C to 50°C.
Considering that the heat of vaporization of water is 539 cal/g, the steam will first release this amount of energy as it condenses at 100°C. After condensation, the water will release more heat as it cools down, following the specific heat capacity of water.
Since the container and water together gained a total of 6300 cal, and in an isolated system, energy is conserved, the steam must have lost 6300 cal during the change of phase and cooling.
This is based on the principle of calorimetry, which states that heat lost by one component of the system must equal the heat gained by another if no heat is lost to the surroundings. Therefore, the correct answer is a. 6,300 cal, assuming there is no heat exchange with the surroundings and all the heat from the steam was transferred to the water and container.