Question

ВОПРОС НА 100 б решите они ваши)) В кастрюлю налили кружку воды при температуре 40С и 4 кружки воды при температуре 30С. Сколько кружек воды при температуре 20С надо еще добавить в кастрюлю, чтобы установилась температура 26С? Теплоемкость кастрюли пренебречь.

Answer 1

Воспользуемся правилом теплового равновесия, согласно которому количество теплоты, принятое холодным телом и отданное тёплым, равны. Массу будем измерять не в кг, а в кружках:
$c*1*(40-26)+c*4*(30-26)=c*m*(26-20)\\14c+16c=6cm\\30c=6cm\\m=5$
Ответ: 5 кружек

Answer 2

Problem Analysis

To solve this problem, we need to determine how many cups of water at a temperature of 20°C should be added to a pot containing 1 cup of water at 40°C and 4 cups of water at 30°C in order to reach a final temperature of 26°C. We can assume that the heat capacity of the pot is negligible.

Solution

To solve this problem, we can use the principle of heat transfer, which states that the heat gained by one substance is equal to the heat lost by another substance. In this case, the heat gained by the cooler water at 20°C should be equal to the heat lost by the warmer water at 40°C and the water at 30°C.

Let's denote the number of cups of water at 20°C that need to be added as x.

The heat gained by the water at 20°C can be calculated using the formula:

Q1 = m1 * c * (Tf - Ti)

Where: - Q1 is the heat gained by the water at 20°C - m1 is the mass of the water at 20°C (which is equal to the number of cups of water at 20°C multiplied by the density of water) - c is the specific heat capacity of water (which is approximately 4.18 J/g°C) - Tf is the final temperature (26°C) - Ti is the initial temperature (20°C)

The heat lost by the water at 40°C and the water at 30°C can be calculated using the same formula:

Q2 = m2 * c * (Tf - Ti)

Where: - Q2 is the heat lost by the water at 40°C and the water at 30°C - m2 is the mass of the water at 40°C and the water at 30°C (which is equal to the sum of the masses of the water at 40°C and the water at 30°C)

Since the heat gained by the water at 20°C should be equal to the heat lost by the water at 40°C and the water at 30°C, we can set up the following equation:

Q1 = Q2

Substituting the formulas for Q1 and Q2, we get:

m1 * c * (Tf - Ti) = m2 * c * (Tf - Ti)

Simplifying the equation, we find:

m1 = m2

Since the mass of the water at 20°C is equal to the mass of the water at 40°C and the water at 30°C, we can set up the following equation:

x * density_of_water = (1 + 4) * density_of_water

Simplifying the equation, we find:

x = 5

Therefore, we need to add 5 cups of water at a temperature of 20°C to the pot in order to reach a final temperature of 26°C.

Answer

To reach a final temperature of 26°C, you need to add 5 cups of water at a temperature of 20°C to the pot.