Question

A) Consider a country with a population of 20 million people. Suppose we need 200,000 MJ/person each year to support a satisfactory UN Human Development Index. How much energy (in MJ) is needed each year by the country? 

B) How much power (in MW) is required?

C) How many 1000 MW power plants are needed?

D) How much energy (in MJ) is needed each day?

E) Suppose the energy is obtained by consuming crude oil with an energy density of 37,000 MJ/m3. How many barrels of crude oil are required each day?

Answer 1

Solution.

A)

$N=20\sdot10^{6}$people;

$W_1=200000\sdot10^{6}J;$

$W=N\sdot W_1;$

$W=20\sdot10^{6}\sdot200000\sdot10^{6}=4\sdot10^{18}J=4\sdot 10^{12}MJ;$

B)

$P=\dfrac{W}{t};$

$t=365\sdot24\sdot3600=31536000s;$

$P=\dfrac{4\sdot 10^{18}}{31536000}=1.27\sdot 10^{11}W=127000MW;$

C)

$P_1=1000MW;$

$K=\dfrac{P}{P_1};$

$K=\dfrac{127000}{1000}=127;$

D)$W_d=\dfrac{W}{D};$

$W_d=\dfrac{4\sdot 10^{12}}{365}=1.1\sdot10^{10}MJ;$

E)

$J=37000MJ/m^3;$

$J=\dfrac{W}{V}\implies V=\dfrac{W}{J};$

$V=\dfrac{1.1\sdot 10^{10}}{37000}=2.7\sdot 10^{5}m^3=1698249US bbl oil;$

Answer: A) $W=4\sdot 10^{12}MJ;$

B)$P=127000MW;$

C)$K=127;$

D)$W_d=1.1\sdot10^{10}MJ;$

E)$V=1698249US bbl oil;$