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a BATH CONTAINS 100 KG OF WATER AT 60 DEGREES CELCIUS. HOT AND COLD TAPS ARE THEN TURNED ON TO DELIVER 20KG PER MINUTE EACH A TEMPERATURE 70 DEGREES CELSIUS AND 10 DEGREES CELSIUS RESPECTIVELY. HOW LONG WILL IT BE BEFORE THE TEMPERATURE IN THE BATH HAS DROPPED TO 45 DEGREES CELCIUS. ASSUME COMPLETE MIXING OF WATER AND IGNORE HEAT LOSSES.

7.5SECONDS

70-10

To find out how long it will take for the temperature to drop to 45 degrees Celsius, we need to consider the heat gained and lost by the water in the bath.

Let's break down the problem:

1. Heat gained by hot water: The hot tap delivers 20 kg of water per minute at a temperature of 70 degrees Celsius. The specific heat capacity of water is approximately 4.18 J/g°C. So, the heat gained by the hot water per minute can be calculated as follows:

Heat gained by hot water = mass of hot water * specific heat capacity * temperature change
= 20 kg * 4.18 J/g°C * (70 - 45)°C

2. Heat gained by cold water: The cold tap delivers 20 kg of water per minute at a temperature of 10 degrees Celsius. So, the heat gained by the cold water per minute can be calculated as:

Heat gained by cold water = mass of cold water * specific heat capacity * temperature change
= 20 kg * 4.18 J/g°C * (45 - 10)°C

3. Heat lost by the water in the bath: We can assume that the heat lost by the water in the bath is equivalent to the heat gained by the hot and cold water, as stated in the problem.

Heat lost by water in the bath = Heat gained by hot water + Heat gained by cold water

Now, we can calculate the time it takes for the temperature to drop to 45 degrees Celsius by dividing the heat lost by the water in the bath by the rate of heat loss per minute:

Time = Heat lost by water in the bath / (heat loss rate of bath water per minute)

Since we are given that the bath initially contains 100 kg of water at 60 degrees Celsius, we need to consider the temperature change from 60 degrees Celsius to 45 degrees Celsius.

I will now calculate the time it will take for the temperature in the bath to drop to 45 degrees Celsius.