I can dispense 300 liters of liquid continuously in one hour from a given temp. of 22*c down to 7*c.
(delta T=15)
How many liters and in what time can I dispense from a temp. of 24*c down to 3*c ? (delia T=21)
To determine the number of liters and the time it takes to dispense liquid from a temperature of 24°C down to 3°C (ΔT = 21°C), we can use the concept of the heat capacity, which is the amount of heat energy needed to raise the temperature of a substance by a certain amount.
First, we need to calculate the heat exchanged (Q) using the formula:
Q = mass × specific heat capacity × ΔT
Since we don't have the mass or the specific heat capacity of the liquid, we need to use the fact that the heat exchanged is proportional to the temperature change. This means we can write:
Q1 / Q2 = ΔT1 / ΔT2
Where Q1 and ΔT1 are the known values (300 liters and 15°C, respectively) and Q2 and ΔT2 are the unknown values (the number of liters and the temperature difference we want to find, respectively).
Let's plug in the values:
300 liters / Q2 = 15°C / 21°C
Cross-multiplying, we have:
Q2 = (300 liters × 21°C) / 15°C
= 4200 liters / 15°C
= 280 liters / °C
Now we need to find the change in temperature (ΔT2 = 21°C) for this new heat exchange rate:
Q2 = mass × specific heat capacity × ΔT2
Rearranging the equation, we get:
mass × specific heat capacity = Q2 / ΔT2
mass × specific heat capacity = 280 liters / °C / 21°C
mass × specific heat capacity = 280 liters / 21°C
mass × specific heat capacity = 13.333 liters / °C
Now, we don't have the specific heat capacity, but we know that it is constant for a given substance. So we can rewrite the equation as:
mass = 13.333 liters / °C / specific heat capacity
To calculate the time it takes to dispense this amount of liquid, we need more information.