Question

За ранее спасибо. Для купания ребёнка в ванночку влили холодную воду массой 20кг при температуре 12 градусов. Сколько горячей воды при температуре 80 градусов нужно добавить в ванночку, чтобы окончательная температура воды стала 37 градусов.

Answer 1

44256435544456 градусов воды

Answer 2

Calculation of Hot Water Needed

To calculate the amount of hot water needed to achieve a final temperature of 37 degrees Celsius in the bathtub, we can use the principle of heat transfer. The heat gained by the cold water should be equal to the heat lost by the hot water.

Let's assume that the initial temperature of the cold water is 12 degrees Celsius, its mass is 20 kg, and the final temperature is 37 degrees Celsius. The initial temperature of the hot water is 80 degrees Celsius.

The heat gained by the cold water can be calculated using the formula:

Q_cold = m_cold * c * (T_final - T_initial)

Where: - Q_cold is the heat gained by the cold water - m_cold is the mass of the cold water - c is the specific heat capacity of water (approximately 4.18 J/g°C) - T_final is the final temperature (37 degrees Celsius) - T_initial is the initial temperature of the cold water (12 degrees Celsius)

The heat lost by the hot water can be calculated using the formula:

Q_hot = m_hot * c * (T_initial - T_final)

Where: - Q_hot is the heat lost by the hot water - m_hot is the mass of the hot water - c is the specific heat capacity of water (approximately 4.18 J/g°C) - T_initial is the initial temperature of the hot water (80 degrees Celsius) - T_final is the final temperature (37 degrees Celsius)

Since the heat gained by the cold water is equal to the heat lost by the hot water, we can set up the equation:

Q_cold = Q_hot

Substituting the formulas for Q_cold and Q_hot:

m_cold * c * (T_final - T_initial) = m_hot * c * (T_initial - T_final)

Simplifying the equation:

m_cold * (T_final - T_initial) = m_hot * (T_initial - T_final)

Now we can solve for m_hot, the mass of the hot water needed.

Let's plug in the given values: - m_cold = 20 kg - T_initial = 12 degrees Celsius - T_final = 37 degrees Celsius - c = 4.18 J/g°C

Calculating the mass of the hot water needed:

20 kg * (37 - 12) = m_hot * (80 - 37)

20 kg * 25 = m_hot * 43

m_hot = (20 kg * 25) / 43

m_hot ≈ 11.63 kg

Therefore, approximately 11.63 kg of hot water at 80 degrees Celsius needs to be added to the bathtub to achieve a final temperature of 37 degrees Celsius.

Please note that this calculation assumes no heat loss to the surroundings and that the specific heat capacity of water remains constant over the temperature range.