Final answer:
To raise the temperature of a 200-liter hot tub from 20°C to 40°C, one would need 16,736,000 J or 16.73 MJ of heat energy, given water's specific heat is 4,184 J/kg°C.
Step-by-step explanation:
To calculate the amount of heat necessary to raise the temperature of a 200-liter hot tub from 20°C to 40°C, we need to use the specific heat of water and the formula for heat transfer, which is Q = mcΔT, where Q is the heat energy, m is the mass, c is the specific heat, and ΔT is the change in temperature. In this case, the specific heat (c) of water is 4,184 J/kg°C. First, we must convert liters to kilograms, knowing that 1 liter of water has a mass of approximately 1 kg, therefore 200 liters equals 200 kg. Then, we apply the formula with a temperature change (ΔT) of 20°C (40°C - 20°C).
The calculation would be Q = (200 kg)(4,184 J/kg°C)(20°C), which yields Q = 16,736,000 J or 16.73 MJ. This is the energy required to heat the water in the hot tub from 20°C to 40°C without considering any heat loss to the environment.