Answer:
4.2g of gasoline
Explanation:
In the problem, you need to give energy to the cup from the combustion of gasoline. The energy you need to give is:
Qcup + QWater + QCopper
As you need to increase (110ºC - 21ºC = 89º = Increase 89K) 89K, the Qcup is:
Qcup = 89K × (47J/K) = 4183J.
You can find Qwater using its specific heat, C (4.18Jg⁻¹K⁻¹), its mass (450mL = 450g) and the change of temperature, 89K:
QWater = CₓmₓΔT
QWater = 4.184Jg⁻¹K⁻¹ ₓ 450g×89K
QWater = 167569J
And Q of Copper, QCu, could be obtained in the same way (Specific heat Cu: 0.387 J/g⁻¹K⁻¹:
QCu = CₓmₓΔT
QCu = 0.387 J/g⁻¹K⁻¹ₓ850gₓ89K
QCu = 29277J
Thus, total heat you need is:
Q = Qcup + QWater + QCopper
Q = 4183J + 167569J + 29277J
Q = 201029J = 201kJ
The combustion of gasoline (Octane) produce 47.8kJ/g (Its heat of combustion). that means to produce 201kJ of energy you require:
201kJ × (1g / 47.8kJ) =
<h2>4.2g of octane = Gasoline you require</h2>
