how many joules are required to heat a frozen can of juice (360 grams) from -5C (the temperature of an overcooled refrigerator to 110C) the highest practical temperature within a microwave oven?
To calculate the amount of energy required to heat the frozen can of juice, we can use the formula:
\(Q = mcΔT\)
Where:
- \(Q\) represents the energy required (in joules)
- \(m\) is the mass of the can of juice (in grams)
- \(c\) is the specific heat capacity of the juice
- \(\Delta T\) is the change in temperature (in Celsius)
First, let's calculate \(c\), the specific heat capacity of the juice. The specific heat capacity is the amount of heat energy required to raise the temperature of a substance by 1 degree Celsius per gram.
Unfortunately, the specific heat capacity of juice is not readily available, but since juice is primarily composed of water, we can use the specific heat capacity of water as an approximation. The specific heat capacity of water is approximately 4.18 joules per gram per degree Celsius.
Now, let's calculate the change in temperature (\(\Delta T\)). We are going from -5°C to 110°C. The change in temperature is \(110°C - (-5°C) = 115°C\).
Next, we convert the mass of the juice from grams to kilograms. \(360\) grams is equal to \(0.36\) kilograms.
Using these values, we can substitute them into the formula:
\(Q = mcΔT\)
\(Q = 0.36 kg \times 4.18 J/g°C \times 115°C\)
Calculating this equation, we get:
\(Q = 179.46\) Joules
Therefore, approximately 179.46 Joules of energy is required to heat the frozen can of juice from -5°C to 110°C.
This is a long but not difficult problem.
q1 = heat to move solid from -5 to zero C.
q1 = mass x specific heat (I assume you will use that of ice) x 5).
q2 = heat to melt solid.
q2 = mass x heat fusion.
q3 = heat to move liquid from zero to 100.
q3 = mass x specific heat liquid x delta T.
delta T = 100
q4 = heat to vaporize liquid to vapor at 100.
q4 = mass x delta Hvap.
q5 = heat to move steam T from 100 to 110 C.
q5 = mass x specific heat steam x 10
total Q = q1 + q2 + q3 + q4 + q5
with sig figs: 1,000,000
So this could be completely wrong lol. But heres my guess...
(360g) * (1.87 j/g C) * (110) = 74052 J
make sure to thumbs down if wrong!