I just can't get any further with this physics problem, can someone help me?
Solar energy is 1500 W/m^2
Can is cylindrical
Capacity beer 500 ml
• Specific heat capacity of beer cB = 4.2 kJ /kgK
Density of beer ρB = 0.995 kg l
• Specific heat capacity of aluminum cAl = 0.89 kJ kgK
• Mass of the aluminum can mAl = 20 g
• Diameter of beer can d = 67 mm
• Height of the beer can h = 17 cm
a) What energy is needed to heat the aluminum of the can from 4 ◦C to 15 ◦C?
b) What energy is necessary to heat the entire can with contents from 4 ◦C to 15 ◦C?
c) How long does it take for the beer can to reach a temperature of 15 ◦C under sunlight?
Thanks for any help. Regards
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The 1500 W/m^2 are not energy at first, but power per surface. Power is energy per unit time.
Based on the information, you can calculate volume and with the specified densities the masses of beer and aluminum can.
The heat capacity calculates the amount of heat, i.e. energy, which is required to heat the mass of beer/alu to a temperature difference.
Depending on which surface of the can is exposed by the sun, you can calculate which heat energy the can absorbs per unit time. The time of heating is then obtained by the quotient of the required thermal energy (for heating from 4 to 15° C.) and the amount of energy per unit of time which transfers the solar radiation.
Q = m • cp • DeltaT
The first two tasks can be solved with the formula. All values are given or you can determine the mass of beer over density and volume.
For the last task you then need t = Q / (p • A), where p is the solar energy.
At A there is still a question of what to expect. Finally, in practice we do not irradiate the can evenly from all sides of the sun. Think about it and write a reason.
The task is otherwise unrealistic. I’d never let my beer stand.