Solving an Ice Cream Conundrum with Temperature Conversion and Salt

[robbie]

Need help on this word problem please. I don't even know where to start with this one.

If you convert 3 kg of ice at -30 degrees C into 3 kg of steam at 120 degrees C. Using this as a model can you explain how we make ice-cream with ingredients of 5 degrees C into soft ice-cream at temperature of -5 degrees C using ice at 0 degrees C as the coolant? (remember the salt)

THANKS.

 

[HallsofIvy]

It might help if you posted the problem as given.
Surely it didn't start "If you convert 3 kg of ice at -30 degrees C into 3 kg of steam at 120 degrees C." That's not a sentence!

If ... then what??

 

[M98Ranger]

Sure, I'd be happy to help with this ice cream conundrum! First, let's break down the problem into smaller steps. The first step is to convert the units of measurement to make the problem easier to understand. So, we need to convert 3 kg of ice at -30 degrees C into 3 kg of steam at 120 degrees C.

To do this, we can use the formula: Q = m * c * ΔT
where Q is the heat energy, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.

Since we are converting from ice to steam, we can use the specific heat capacity for water, which is 4.18 J/g°C. So, the first step would be to calculate the heat energy required to convert 3 kg of ice to water at 0 degrees C.

Q = (3 kg) * (4.18 J/g°C) * (30°C) = 376.2 kJ

Next, we need to calculate the heat energy required to convert 3 kg of water at 100 degrees C to steam at 120 degrees C.

Q = (3 kg) * (4.18 J/g°C) * (20°C) = 250.8 kJ

Now, to make ice cream using the same principles, we need to take the ingredients at 5 degrees C and convert them to -5 degrees C. To do this, we can use the same formula, but this time the ΔT will be negative since we are going from a higher temperature to a lower temperature.

Q = (m) * (4.18 J/g°C) * (-10°C)

To make the ice cream, we need to remove heat energy from the ingredients, which is why the ΔT is negative. Now, we need to figure out how much heat energy we need to remove to get the ingredients to -5 degrees C.

Q = (m) * (4.18 J/g°C) * (-10°C) = 50 J

Now, the last step is to use ice at 0 degrees C as the coolant. To make the ice cream, we need to use a mixture of ice and salt. The salt lowers the freezing point of water, making it colder than 0 degrees C. This will help us achieve the desired temperature of -5 degrees C for our ice cream.