A partly filled barrel 300 lb water and

Answered question

2022-05-14

A partly filled barrel 300 lb water and 100 lb of ice at 32ºF. How many pounds of steam at 212ºF must be run into the barrel to bring its contents up to 80ºF?

Answer & Explanation

Nick Camelot

Nick Camelot

Skilled2023-05-14Added 164 answers

To solve the problem, we need to determine the amount of steam, in pounds, that must be added to the barrel to raise the temperature of its contents from 32ºF to 80ºF.
Let's assume that x represents the pounds of steam we need to add.
To find the amount of heat required, we can use the principle of heat transfer:
Heat gained by water+Heat gained by ice+Heat gained by steam=0
Now, let's calculate each term separately:
1. Heat gained by water:
The specific heat capacity of water is 1 calorie/gram/ºC. Since we are working with pounds, we need to convert the given values into pounds. There are 454 grams in a pound. Also, the temperature change is from 32ºF to 80ºF, which is an increase of 48ºF. The equation for heat gained by water is:
Heat gained by water=weight of water×specific heat capacity×temperature change
Heat gained by water=300×(1454)×48
2. Heat gained by ice:
The specific heat capacity of ice is also 1 calorie/gram/ºC. Using the same conversion factor for pounds and considering a temperature change from 32ºF to 80ºF, we have:
Heat gained by ice=weight of ice×specific heat capacity×temperature change
Heat gained by ice=100×(1454)×48
3. Heat gained by steam:
The latent heat of vaporization for water is the amount of heat required to convert water from a liquid to steam at its boiling point. The latent heat of vaporization for water is approximately 970 BTU/pound. Again, we need to convert the given temperatures into degrees Celsius:
Heat gained by steam=weight of steam×latent heat of vaporization
Heat gained by steam=x×970
Now, substituting these values into the initial equation, we have:
300×(1454)×48+100×(1454)×48+x×970=0
Simplifying the equation:
300454×48+100454×48+970x=0
To solve for x, we can isolate the variable:
970x=300454×48100454×48
x=300454×48×1970100454×48×1970
Calculating this expression will give us the value of x, which represents the pounds of steam that need to be added to the barrel to raise its contents to 80ºF.

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