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Re:Which is actually cheaper, soda or ice?
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Ask The Mythbusters
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· Score: 3, Interesting
I'll take a crack at answering this question. Please note, though, that this estimate makes a lot of assumptions. All assumptions are listed below.
1. You purchase a 20-oz soda (or 600 mL) from McDonalds. Let's assume they fill the cup to the top with ice, and let's assume that if you melted the ice, you'd displace 300 mL of the cup with water. (i.e. in order to "save money", they give you 300 mL of soda and 300 mL of water, instead of a full 600 mL of soda.)
2. How much energy does it take to cool 300 mL of room temp (25 C) water to, say, -10 C? To answer this question, we need to break it up into 3 parts:
a. What is the energy required to cool water from 25 C to 0 C? Using the equation Q = c m deltaT, where c is the specific heat of water (1 cal/g C), m is the mass of water (300 g, assuming a density for water of 1 g/mL) and deltaT is the change in temperature (25 C), the energy required is 7,500 cal.
b. What is the energy required to freeze water? The specific latent heat of fusion for water is 80 cal/g. So 300 g of water would require 24,000 cal.
c. What is the energy required to cool water from 0 C to -10 C? Using the same equation as (a) above, except using 0.48 cal/g C as the specific heat of ice, and 10 C as the deltaT, the energy required would be 1,440 cal.
This is a total energy requirement of 32,940 cal. There are 859,845 cal in 1 kwh (kilowatt hour). So it would require approximately 0.038 kwh to freeze this quantity of ice.
3. What does this amount of electricity cost? Assuming that electricity costs 10 cents per kwh (a high estimate), and that the freezer used is only about 10% efficient (probably a high estimate as well), then it would cost about 4 cents.
4. What does an equivalent amount of soda cost? A quick cursory search on Google found that 5 gal of Coca-Cola syrup can be had for $40.00. This is mixed 4.5 parts carbonated water to 1 part syrup, so the effective amount of soda produced by this 5 gal container is 22.5 gal. This comes out to be about 47 cents per liter; 300 mL would cost 14 cents. (This assumes that the cost of carbonated water, and the electricity to precool the syrup and water, is zero. So the effective price of the soda is actually higher.)
5. Conclusion: McDonalds saves 10 cents by filling your cup brim full with ice. With billions served, that comes out to a lot of money!
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I'll take a crack at answering this question. Please note, though, that this estimate makes a lot of assumptions. All assumptions are listed below.
1. You purchase a 20-oz soda (or 600 mL) from McDonalds. Let's assume they fill the cup to the top with ice, and let's assume that if you melted the ice, you'd displace 300 mL of the cup with water. (i.e. in order to "save money", they give you 300 mL of soda and 300 mL of water, instead of a full 600 mL of soda.)
2. How much energy does it take to cool 300 mL of room temp (25 C) water to, say, -10 C? To answer this question, we need to break it up into 3 parts:
a. What is the energy required to cool water from 25 C to 0 C? Using the equation Q = c m deltaT, where c is the specific heat of water (1 cal/g C), m is the mass of water (300 g, assuming a density for water of 1 g/mL) and deltaT is the change in temperature (25 C), the energy required is 7,500 cal.
b. What is the energy required to freeze water? The specific latent heat of fusion for water is 80 cal/g. So 300 g of water would require 24,000 cal.
c. What is the energy required to cool water from 0 C to -10 C? Using the same equation as (a) above, except using 0.48 cal/g C as the specific heat of ice, and 10 C as the deltaT, the energy required would be 1,440 cal.
This is a total energy requirement of 32,940 cal. There are 859,845 cal in 1 kwh (kilowatt hour). So it would require approximately 0.038 kwh to freeze this quantity of ice.
3. What does this amount of electricity cost? Assuming that electricity costs 10 cents per kwh (a high estimate), and that the freezer used is only about 10% efficient (probably a high estimate as well), then it would cost about 4 cents.
4. What does an equivalent amount of soda cost? A quick cursory search on Google found that 5 gal of Coca-Cola syrup can be had for $40.00. This is mixed 4.5 parts carbonated water to 1 part syrup, so the effective amount of soda produced by this 5 gal container is 22.5 gal. This comes out to be about 47 cents per liter; 300 mL would cost 14 cents. (This assumes that the cost of carbonated water, and the electricity to precool the syrup and water, is zero. So the effective price of the soda is actually higher.)
5. Conclusion: McDonalds saves 10 cents by filling your cup brim full with ice. With billions served, that comes out to a lot of money!