# Physics

Monique has 250 grams of water in a blue insulated cup at 15 °C. In a red insulated cup, she has some water that is at 75 °C. When she mixes the cold water into the warm water, the temperature of all the water reaches 35 °C. (The specific heat of water is 4.84 J g^−1 °C^−1.)

a) Write an algebraic equation that represents the heat gained by the cold water. Write the number equation (with units!) for the heat gained by the cold water. Calculate the heat.

b) Write an algebraic equation that represents the heat lost by the cold water. Write the number equation (with units!) for the heat lost by the cold water. Calculate the heat.

c) How are the heat gained by the cold water and the heat lost by the warm water related? Answer with words and a math equation.

d) Determine the mass of the warm water initially in the red cup.

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1. Gained by cold = (4.84 J g^−1 °C^−1)( 250 g)(35 °C - 15 °C)
= 24,200 Joules

Lost by hot (you mean) = (4.84 J g^−1 °C^−1) (m grams) (75 °C - 35 °C)

Lost by hot = gained by cold if insulation is perfect
24,200 Joules = (4.84 J g^−1 °C^−1) (m grams) (75 °C - 35 °C)
m = [24,200 /( 4.84 * 40)] grams
= 125 grams which you could have said at the start because its temperature change is twice as much as the cold so it needs half the mass.

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2. thanks so much Damon :D

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