Question

The conventional coal-fired power plant has an efficiency of about 33%. Assuming that all the coal in Example 8–3 were used to generate electricity (it was not), estimate the time until exhaustion, if the efficiency were raised to 40%.In 2004, the international consumption of coal for energy was 120.8 EJ (EIA, 2006). Assuming the 2004 demand remains constant, how long will world reserves last? The average world consumption of coal-based energy increased 5.15% per year from 2000 to 2004. If that rate of increase remains constant, how long will world reserves last?

Answer 1

Answer:

See attachment for detailed answer.

Explanation:

Answer 2

Answer:

163.9 years; 44.7 years

Explanation:

The calculation of the number of years that the world reserves will last is shown below:

If there is a constant demand for coal, then the number of years the world reserve will last is:

19800 EJ/(120.8 EJ/year) = 163.9 years

If the demand for coal increases at the rate of 5.15%, then, the number of years the reserve will last is:

$19800 EJ = 120.8 EJ/year[\frac{(1+0.0515)^{n}-1}{0.0515}]$

Further simplification and rearrangement lead to:

$\frac{19800*0.0515}{120.8} = (1.0515)^{n} - 1$

$8.44 = 1.0515^{n} -1$

$1.0515^{n} = 9.44$

Taking the logarithm of both sides, we have:

$log (1.0515^{n}) = log (9.44)$

$n log (1.0515) = 0.975$

n (0.02181) = 0.975

n = 0.975/0.02181 = 44.7 years