100k views
2 votes
How much heat is needed to raise the temperature of a 200-liter hot tub from 20°C to 40°C? The specific heat of water is 4,184 J/kg°C.

User Costo
by
7.7k points

1 Answer

5 votes

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.

User Mayank Mahajan
by
8.0k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.