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How much energy must be added to a bowl of 125 popcorn kernels in order for them to reach a popping temperature of 175 degrees Celsius? Assume that their initial temperature is 21 degrees Celsius, that the specific heat capacity of popcorn is 1650J/kg degrees Celsius, and that each kernel has a mass of .105 g.
Q=(0.013125)(1650)(154)
Q=3335.0 J/kg degree Celsius
I got the 0.013125 by making 0.105g into kilograms them multiplying that number by 125. I got the 154 by subtracting 175-21.
Calculate the mass of 125 pocorn kernels. Call it M.
Then use the equation for heating something with constant specific heat.
Q = M C * (delta T)
delta T is the temperature change.
That is an equation you should remember and be prepared to use the next time you see this kind of a problem.
Solve for the heat required, Q.
To calculate the amount of energy that needs to be added to the popcorn kernels, we need to use the formula:
Q = mcΔT
Where:
Q = Amount of energy (in joules)
m = Mass of the popcorn kernels (in kilograms)
c = Specific heat capacity of popcorn (in Joules per kilogram per degree Celsius)
ΔT = Change in temperature (final temperature - initial temperature) (in degrees Celsius)
Given:
Initial temperature (T1) = 21 degrees Celsius
Final temperature (T2) = 175 degrees Celsius
Specific heat capacity of popcorn (c) = 1650J/kg degrees Celsius
Mass of each kernel (m) = 0.105g = 0.105 * 10^-3 kg
First, we need to calculate the change in temperature:
ΔT = T2 - T1 = 175 - 21 = 154 degrees Celsius
Now we can substitute the values into the formula and calculate the amount of energy:
Q = (0.105 * 10^-3 kg) * (1650 J/kg degrees Celsius) * (154 degrees Celsius)
Q = 2.98 J
Therefore, approximately 2.98 Joules of energy must be added to the bowl of popcorn kernels for them to reach a popping temperature of 175 degrees Celsius.
To calculate the amount of energy required to increase the temperature of the popcorn kernels, you can use the equation:
Q = mcΔT
Where:
Q is the amount of energy required (in joules)
m is the mass of the popcorn kernels (in kilograms)
c is the specific heat capacity of popcorn (in joules per kilogram per degree Celsius)
ΔT is the change in temperature (in degrees Celsius)
First, convert the mass of the popcorn kernels from grams to kilograms:
0.105 g = 0.105 / 1000 kg = 0.000105 kg
Next, determine the change in temperature:
ΔT = final temperature - initial temperature
= 175°C - 21°C
= 154°C
Now, plug in the values into the formula:
Q = (0.000105 kg) x (1650 J/kg°C) x (154°C)
Calculating this expression gives us the amount of energy required to heat up the popcorn kernels to the desired temperature.