1. A researcher studying the nutritional value of a new candy places a 5.90-gram

Question

1. A researcher studying the nutritional value of a new candy places a 5.90-gram sample of the candy inside a bomb calorimeter and combusts it in excess oxygen. The observed temperature increase is 2.97 °C. If the heat capacity of the calorimeter is 29.00 kJ·K–1, how many nutritional Calories are there per gram of the candy?

2.An experimental spacecraft consumes a special fuel at a rate of 314 L/min. The density of the fuel is 0.830 g/mL and the standard enthalpy of combustion of the fuel is –47.3 kJ/g. Calculate the maximum power (in units of kilowatts) that can be produced by this spacecraft. 1 kW = 1 kJ/s

Explanation / Answer

now

heat = heat capacity x temp change

so

Heat = 29 x 2.97

heat = 86.13 kJ

now

we know that

1 kCal = 4.184 kJ

so

Heat = 86.13 / 4.184 kcal

Heat = 20.585564 kcal

now

nutrional value per gram = heat / mass

nutritional value per gram = 20.585564 / 5.90

nutritional value per gram = 3.489 kcal / g

= 3489 cal/ g

so

the nutritional value is 3489 cal/ gram

2)

now mass rate is given by

mass rate = volume rate x density

given

volume rate = 314 x 1000 ml / min

density = 0.83 g/ml

so

mass rate = 314 x 1000 x 0.83

mass rate = 260.62 x 1000 g / min

mass rate = 260.62 kg / 60 s

mass rate = 4.343666 kg / s

now

power = enthalpy x mass rate

power = 47.3 x 4.342666 x1000

power = 205455 kJ/s

power = 205455 kW

so

the power is 205455 kW

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