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Answer :
To achieve a final bath temperature of 36°C, equations based on the principle of conservation of energy must be used to calculate the required masses of hot and cold water. This type of problem is known as a thermal math problem in the field of thermal physics.
Solving a Thermal Math Problem
When mixing hot and cold water to achieve a desired equilibrium temperature, thermal energy is transferred until the temperatures equalize. The total mass of the mixture is given as 186 kg, and we aim for a final temperature of 36°C. Applying the principle of conservation of energy, the heat gained by the cold water must equal the heat lost by the hot water. The mass of hot water (mh) and cold water (mc) can be related by this formula:
mc(36°C - 12°C) = mh(50°C - 36°C)
Given that mc + mh = 186 kg, we can solve these equations simultaneously to find the mass of hot and cold water needed. This is a common type of problem encountered in thermal physics.
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