Question

3. A solar greenhouse has three twenty-lb steel barrels as thermal storage. The volume of the barrels is 55 gallons. The owner filled the first one barrel with 55 gallons of water, filled the second half full (27.5 gallons), and left the third empty. If the sun adds 500 BTUs of heat to each barrel, how much will each barrel warm up? A gallon of water weights 8.34 lb, and a gallon in volume is equal to 0.13368 cubic feet. (9 points) Specific heat (Btu/lb F) density (lb/cu.ft) 0.24 Air Water Steel 0.075 62.0 489.0 0.12

Answer 1

Volume of Barrel in cubic feet = $55*0.13368= 7.3524$ cubic feet

Barrel1

1. Completely filled with water: $62.0*7.3524= 458.7$ lb.

2. Weight of barrel: $20lb$

Barrel2

1. Half filled with water : $3.6762*62.0 =229.35lb$ .

2. Half filled with air : $3.6762*0.075 = 0.275715 lb$

3. Weight of barrel: $20lb$

Barrel3

1. Completely filled with air: $7.3524*0.075=0.55143lb$

2. Weight of barrel: $20lb$

Formula to be used: ${mass}*{specific heat}*{rise in temperature}= BTU$

for Barrel1

$\Delta F = 500/(458.7 + 20*0.12)$

$\Delta F = 1.0836$answer

for Barrel2

$\Delta F = 500/(229.35+0.275715*0.24 + 2.4)$

$\Delta F = 2.15688$answer

for Barrel3

$\Delta F = 500/(0.55143*0.24 + 2.4)$

$\Delta F = 197.4455$answer