A biology experiment requires the preparation of a water bath at 37.0°C (body temperature). The temperature of the cold tap water is 22.0°C, and the temperature of the hot tap water is 55.0°C. If a student starts with 70.0 g of cold water, what mass of hot water must be added to reach 37.0°C?

75gm

mass cold water x specific heat x (Tfinal-Tinitial) + mass hot water x specific heat x (Tfinal-Tinitial) = 0

Solve for mass hot water.

To find the mass of hot water needed, we can use the principle of conservation of energy, which states that the heat lost by the hot water will be equal to the heat gained by the cold water.

The formula we can use is:

(mass of hot water) x (initial temperature of hot water - final temperature) = (mass of cold water) x (final temperature - initial temperature of cold water)

Let's use this formula to solve the problem:

Let:
Mass of hot water = x grams

Plugging in the values:
(x) x (55.0°C - 37.0°C) = (70.0 g) x (37.0°C - 22.0°C)

Simplifying:
18x = 70.0 g x 15.0°C

Dividing both sides by 18:
x = (70.0 g x 15.0°C) / 18

Evaluating:
x ≈ 58.3 g

Therefore, approximately 58.3 grams of hot water must be added to reach a temperature of 37.0°C.

To find the mass of hot water needed to reach 37.0°C, we can use the principle of energy conservation. The energy lost by the hot water must be equal to the energy gained by the cold water to reach a thermal equilibrium at 37.0°C.

First, let's calculate the energy lost by the hot water. We can use the formula:

Energy lost = mass × specific heat capacity × temperature change

The specific heat capacity of water is approximately 4.18 J/g°C. The initial temperature of the hot water is 55.0°C and the final temperature is 37.0°C, so the temperature change is 55.0°C - 37.0°C = 18.0°C.

Therefore, the energy lost by the hot water is:
Energy lost = mass of hot water × 4.18 J/g°C × 18.0°C

Now, let's calculate the energy gained by the cold water using the same formula. The specific heat capacity is still 4.18 J/g°C, and the initial temperature of the cold water is 22.0°C, and the final temperature is 37.0°C, so the temperature change is 37.0°C - 22.0°C = 15.0°C.

The energy gained by the cold water is:
Energy gained = 70.0 g × 4.18 J/g°C × 15.0°C

Since energy is conserved, the energy lost by the hot water is equal to the energy gained by the cold water:

mass of hot water × 4.18 J/g°C × 18.0°C = 70.0 g × 4.18 J/g°C × 15.0°C

Simplifying the equation, we find:

mass of hot water = (70.0 g × 4.18 J/g°C × 15.0°C) / (4.18 J/g°C × 18.0°C)

mass of hot water = 875 g

Therefore, to reach 37.0°C, you need to add 875 g of hot water to 70.0 g of cold water.