A 5.00-grain aspirin tablet has a mass of 320 mg. For how many kilometers would the energy equivalent of this mass power an automobile? Assume 12.75 km/L and a heat of combustion of 3.65x10^7 J/L for the gasoline used in the automobile.
E=mc²=320•10⁻⁶•9•10¹⁶=2.88•10¹³ J
E/3.65•10⁷=2.88•10¹³ /3.65•10⁷=7.9•10⁵ L
7.9•10⁵•12.75=1•10⁷ km
Thank you!
To determine the energy equivalent of the mass of the aspirin tablet, you would first need to convert the mass from grains to kilograms.
1 grain = 64.79891 milligrams (mg)
5.00 grains = 5.00 * 64.79891 mg = 323.99455 mg
Now, convert the mass of the aspirin tablet to kilograms:
323.99455 mg = 323.99455 * 10^-3 g = 0.32399455 g
0.32399455 g = 0.32399455 * 10^-3 kg = 0.00032399455 kg
Next, you need to find the energy equivalent of this mass. Use the equation:
Energy equivalent = mass * heat of combustion
Energy equivalent = 0.00032399455 kg * 3.65x10^7 J/L
However, the heat of combustion is given in J per L (J/L), but we need it in J per km (J/km) to determine the total distance the energy would power the automobile.
To convert J/L to J/km, you need to divide the given value by the fuel efficiency of the automobile.
Fuel efficiency = 12.75 km/L
So, divide the heat of combustion by the fuel efficiency:
3.65x10^7 J/L / 12.75 km/L = 2.86274509804x10^6 J/km
Finally, multiply the energy equivalent by the conversion factor to determine how many kilometers the energy equivalent of the aspirin tablet would power the automobile:
Energy equivalent = 0.00032399455 kg * 2.86274509804x10^6 J/km
Calculating this, you would get the distance the energy equivalent of the aspirin tablet can power the automobile.