Answer:
319 is the minimum number of fuel canisters.
Explanation:
[tex]Q=mc\Delta T[/tex]
Where:
Q = heat absorbed or heat lost
c = specific heat of substance
m = Mass of the substance
ΔT = change in temperature of the substance
Mass of water = 5.0 kg = 5000 g
Specific heat of water = c = 4.184 J/g°C
ΔT = change in temperature of the water during boiling ;p
= 100°C - 25°C = 75°C
Heat absorbed by 5000 g of water = Q
[tex]Q=5000 g\times 4.184J/g^oC\times 75^oC=1,569,000 J[/tex]
1 J = 0.001 kj
Q =1,569,000 × 0.001 kJ = 1,569 kJ
Heat required in 12 days, Q' = 1,569 kJ × 12 = 18,828 kJ
The standard heat of formation of propane at 25°C = -103.85kJ/mol
The standard heat of formation of 1 gram of propane at 25°C :
=[tex]\frac{-103.85 kJ/mol }{1 mol\times 44 g/mol}=-2.3602 kJ/g[/tex]
Heat released on burning of 1 grams of propane = 2.3602 kJ
Let the number of canister having 25 g of propane be x.
Total mass of propane , M= 25x
M amount of propane will give Q' amount of heat.
[tex]25x \times 2.3602 kJ/g=Q'[/tex]
[tex]25x\times 2.3602 kJ/g=18,828 kJ[/tex]
[tex]x=\frac{18,828 kJ}{25x\times 2.3602 kJ}=319.09\approx 319[/tex]
319 is the minimum number of fuel canisters.