Please helpppppppppppppppppppppppppppp

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To determine how much water at 82 degrees Celsius should be added to 1.00 kg of water at 14 degrees Celsius to achieve a final temperature of 36 degrees Celsius, the principle of heat transfer must be applied. The equation qgained = -qlost is essential for solving this problem, where the heat gained by the cooler water equals the heat lost by the hotter water. The discussion emphasizes using ratios and the specific heat formula to find the correct mass of water needed. A calculation example illustrates that adding 1 kg of water at 82 degrees would result in a temperature of 50 degrees, indicating that less than 1 kg is required. Understanding the heat transfer formula is crucial for accurately solving this type of problem.
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Homework Statement



How much water at 82 degrees celsius must be added to 1.00kg of water at 14 degrees celsius to give it a final temperature of 36 degrees celsius

Homework Equations



qgained=-qlost??

The Attempt at a Solution


finding the resulting temperature, never works out for me please help
 
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If added 1 kg of water at 16 degress to the 1 kg of water at 14 degrees, what would you expect the temperature of the resulting 2 kg of water to be?
 
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Suppose it takes X joules of energy to raise 1Kg of water 1 degree.
You need to increase 1Kg of water by 36-14 = 22 degrees.
You are going to do this by adding water that is 82-14 = 68 degrees hotter.
Then it's just a matter of ratios.

Suppose you added 1Kg it would end up at half way between 14 and 86 = 14 + (86-14)/2 = 50deg so you need less than 1kg
 
Where is your work?

Perhaps to get started, are you aware of this formula?
<br /> m_1 c_1 \left( {T_1 - T_F } \right) = m_2 c_2 \left( {T_F - T_2 } \right)<br />
 
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