Question

В ванной смешали 30 кг горячей воды при температуре 86'С и 20кг холодной воды при температуре 4'С принебрегая потерями энергии на нагревание ванны и окружающей среды, определите установившуюся температуру в ванне. Помогие пожалуйста с подробным решением. Спасибо

Answer 1

Q1 = Q2 
cm1(t - t1) = cm2(t2-t) 
m1t - m1t1 = m2t2 - m2t
t = (m2t2+m1t1)/ m1+m2 = (30*86 + 20*4)/ 50 кг = 53,2 °с

Answer 2

Problem Analysis

To determine the final temperature of the mixed water in the bathtub, we need to apply the principle of conservation of energy. The total heat gained by the cold water should be equal to the total heat lost by the hot water. We can use the equation Q = mcΔT, where Q is the heat gained or lost, m is the mass of the water, c is the specific heat capacity of water, and ΔT is the change in temperature.

Solution

Given: - Mass of hot water (m1) = 30 kg - Initial temperature of hot water (T1) = 86°C - Mass of cold water (m2) = 20 kg - Initial temperature of cold water (T2) = 4°C

To find the final temperature (Tf) of the mixed water, we can use the equation:

Q1 + Q2 = 0

where Q1 is the heat lost by the hot water and Q2 is the heat gained by the cold water.

Let's calculate the heat lost by the hot water (Q1) and the heat gained by the cold water (Q2).

Calculation

First, we need to calculate the heat lost by the hot water (Q1): Q1 = m1 * c * ΔT1

where c is the specific heat capacity of water and ΔT1 is the change in temperature for the hot water.

Next, we calculate the heat gained by the cold water (Q2): Q2 = m2 * c * ΔT2

where ΔT2 is the change in temperature for the cold water.

Since the final temperature (Tf) is the same for both the hot and cold water, we can set ΔT1 = Tf - T1 and ΔT2 = Tf - T2.

Now, let's substitute the values into the equations and solve for Tf.

Calculation Continued

Using the equation Q1 + Q2 = 0, we have: m1 * c * (Tf - T1) + m2 * c * (Tf - T2) = 0

Substituting the given values: 30 * c * (Tf - 86) + 20 * c * (Tf - 4) = 0

Simplifying the equation: 30 * c * Tf - 30 * c * 86 + 20 * c * Tf - 20 * c * 4 = 0

Combining like terms: 50 * c * Tf - 30 * c *