Would there be sufficient energy to raise the temperature of all the ethanol to its boiling point? (read explanation)
A 355 mL can containing coke contains 140.Cal. per can. If all the energy associated w the can of soda were transferred to 1.2 x 10^4 g of ethanol (drinking alcohol) at 23°C, would there be sufficient energy to raise the temperature of all the ethanol to its boiling point? The boiling point of ethanol is 351 K.
In this problem, we are looking at transferring heat from one object to another because the water lost by the can will be gained by the ethanol. The energy from the can is given so we need to know the formula for the heat needed to raise the temperature of the ethanol from 23 deg C to 78 deg C (converted from Kelvin by subtracting 273). The equation for calculating the heat (i.e. energy) associated with a temperature change is
q = m * s * deltaT
where m is the mass of the substance, s is the specific heat of the substance, and deltaT is the change in temperature. The specific heat of ethanol is 0.58 cal/g K (note the lower case c; 1 Cal = 1000 cal)
Now, we can calculate the ammount of energy needed to
q = (1.2x10^4 g)(0.58 cal/gK)(78-23 degC)
q = 382800 cal
convert from cal to Cal by dividing by 1000
q = 383 Cal
Since 383 Cal are needed and we only have 140 Cal of energy, there is not enough to heat all of the ethanol to the boiling point.