I\'ve tried this question but I\'d like to know whether I\'ve done it right or n

Question

I've tried this question but I'd like to know whether I've done it right or not. Anyone who can do this, please leave a solution.
Whilst out camping with some friends you are inspired to construct a parabolic solar cooker like the one pictured. You have a cardboard dish with a 30cm radius and an apparatus to hold a pot that can hold over 1 liter of water. As users of the solar cooker, you and your friends decide that unless it can boil a 1 liter pot of water in 30 minutes starting from an ambient of 25Celcius, it isn't worth going to the trouble of building the solar cooker. You are able to optimally tilt the dish towards the sun and it is a clear day with the sunlight having a power density of 1 kW/m^2. Being the resident renewable energy expert your friends decide that you are in charge of building the solar cooker. You then begin to search through what materials you have with you.
a) You have Aluminium foil with you and decide to cover the inside of the dish with the foil estimating the reflectivity of the foil to be 70%. Based on this estimate will the water boil in 30minutes, starting from ambient?

Explanation / Answer

Let's start by first finding how much energy it will take to boil the water. (we'll ignore the pot because the energy to heat it will be negligible to the energy needed to heat water.)
To find that we need to use the equation:
Q=cmT, where Q is the energy needed, m is the mass of the water, c is the specific heat of water, and T is the change in temperature.

The specific heat of water is 4181.3 J/(kg·K)

1 L of water has a mass of about 1 kg

And water boils at 100 C, giving us a T of 75 C (also K)

Plugging that all in gives us:

Q=4181.3 J/(kg·K) * 1 kg * 75 K = 314000 J

Now let's find out water power we need to boil the water in thirty minutes. Since power is energy divided by time we take

Power = 314000 J / 1800 s (30 min.) = 174.4 W

So as long as the oven can deliver 174.4 W to the pot, it will boil.

Let's find out how much energy the oven will deliver. Since a parabola bounces everything that strikes it into its center, the power delivered to the pot will be equal to 70% of the sun power hitting the dish.

The dish is .30 m in diameter, giving it an area of *(.30 m)2 = .283 m2

With the sun giving 1 kW/m^2, we get a power of

power = 1 kW/m^2*.283 m2= 283 W that hits the dish, but only 70% of that gets reflected. That gives us a power of:

power = .7 * 283 W = 198 W

And since 198 W > 174.4 W the water boil in less than 30 min.

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.