Question

On a 10 day wilderness expedition you'll need to heat 4.0kg of water to the boiling point each day. The air temperature will average 25°C. You have available canisters of compressed butane C4H10 fuel, which you'll burn to heat the water. Each canister has 75.g of butane in it. What is the minimum number of fuel canisters you must bring? The standard heat of formation of butane at 25°C is −125.7/kJmol.

Answer 1

Explanation:

It is known that relation between heat energy, mass and temperature change is as follows.

                q = $mC \times \Delta T$

where,   C = specific heat of water (in given case) = 4.184 $kJ/kg ^{o}C$

              m = mass

          $\Delta T$ = change in temperature

Therefore, calculate the heat energy as follows.

              q = $mC \times \Delta T$

                 = $4 kg \times 4.184 kJ/kg^{o}C \times (100 - 25)^{o}C$

                =  1255.2 kJ/day

For 10 days, total heat required is as follows.

                $10 \times 1255.2$

               = 12552 kJ

It is known that the value of standard enthalpy of combustion of butane is -49.5 kJ/g.

Therefore, combustion of 1 gm of butane will be 49.5 kJ. Hence, total amount of butane required will be as follows.

                  $\frac{12552 kJ}{49.5 kJ/g}$

                     = 253.57 g

As it is given that 1 canister of butane contains 75 g butane. Hence, no. of canisters required are as follows.

         No. of canisters required = $\frac{253.57}{75}$  

                                                    = 3.38

                                                    = 4 (approximately)

Thus, we can conclude that minimum number of fuel canisters you must bring are 4.