Maths problems

Question

the solar energy falling on one square centimeter of the earth is 1.93 calories per minute.
if 1 kW = 239 calories per second , how many kilowatts per square meter fall on the earth?
round answer to 3 significant digits.

note : 1m^2 = 1 x 10^4 cm^2

Answer 1

Using conversion factor,

1.93 cal/(min x cm²) x (1 min/ 60 sec) x (10⁴ cm²/ 1 m²) x (1 KW x sec/ 239 cal) = 1.3458...

Therefore, 1.35 KW/m²

Answer 2

Hi Danish,

 

Let's first convert calories / minute to kW and then convert square centimeters to square meters.

 

(1.93 cal / min) * (1 min / 60 s) ≈ 0.0322 cal / s

 

I write out the decimal form, but I perform every calculation again to ensure precision.

 

(0.0322 cal / s) * (1 kW / 239 cal/s)  ≈ 0.000135 kW / cm^2

 

I added back the per square centimeter because I did not want to confuse myself when typing out the units earlier.

 

(0.000135 kW/cm^2) * (10^4 cm^2 / m^2) ≈ 1.35 kW / m^2

 

Hope this helps!

Answer 3

We convert 1.93 cal/min to cal/sec: 1.93cal/60sec = 0.03217 cal/sec. Using  1 kW = 239 cal/sec, let's find out how many kW is 0.03217 cal/sec by using proportion: (1kW/239cal/sec) = (x KW/0.03217 cal/sec). x = 0.03217/239=

0.000134589 per sg cm, or to find for sq m multiply by 10^4, or move dec. point 4 places to the right and get the answer: 1.346 kW. 

 

 

Regina G