ENVI3114/5707 Energy and the Environment
Question 1: (6 points)
Consider a combined cycle power plant (gas turbine and a steam turbine) burning natural gas as
follows:
Hot gas temperature = 1100 ºC
Cold gas temperature = 400 ºC
Real efficiency factor of both gas and steam turbine (as a fraction of Carnot efficiency) = 0.6
Inlet temperature for steam turbine = 380 ºC
Outlet temperature for steam turbine = 50 ºC
Greenhouse coefficient of natural gas = 53 Gg of CO2 / PJ.
Calculate:
a) Carnot and real efficiency of gas turbine alone.
b) Carnot and real efficiency of steam turbine alone.
c) Total effective efficiency of gas to electricity conversion (gas and steam turbines combined,
ignore the 20 degrees heat loss between the gas turbine outlet and the steam turbine inlet).
d) GHG emissions from generating 8 GWh of electricity (measured at the power plant).
Question 2: (6 points):
Compare the total costs to the consumer, the greenhouse gas emissions, and the electricity use for four
different consumer uses of electricity over a time period of 5 years:
a) a 60 W incandescent light bulb (price $2.00, typical lifetime of 1000 hours), bulb on for 4 hrs
24 minutes per day;ENVI3114/5707 Calculation Assessment 2024 2 Copyright © (2024), The University of Sydney
b) an 9 W LED bulb ($8, typical lifetime of 8000 hours), lighting duration as in part a);
c) the clock on a microwave, with consumption of 15 W all the time;
d) the microwave in operation (1200 W electrical power), for 10 minutes per day, every day for
5 years.
Assume that the electricity is generated from black coal at a cost to the consumer of 24 cents per kWh.
Note that you can use the following information: generation of 1 MWh of electricity from black coal
produces 1.0 t of CO2-e. Ignore the capital cost of the clock and microwave and ignore associated
embodied emissions for all cases.
Question 3: (5 points)
An island community of 2000 people wants to install some wind turbines to meet some of their
electricity needs. Each person uses on average 5 kWh per day, and the peak load is low at 500 We
per person. There is no restriction on the number of wind turbines, but the length of the blades is
restricted to 20 m for aesthetic reasons. [Since bigger turbines are more cost effective, you can assume
this maximum blade size is used.] The turbines operate at 66% of the theoretical ideal wind-power
efficiency of 59% (see the equation in the lecture notes), and the electrical conversion efficiency is a
further 95%. You can assume that the remaining electricity is supplied by a diesel-fired back-up
generator and that if there is excess wind electricity generated it can be stored for later use with no
losses. Find the following:
a) the yearly total electrical energy required for the island.
b) the peak electrical capacity (total load) required for the island.
c) the number of turbines (to the nearest integer, eg. 10.1 turbines is close enough to 10) required to
meet the peak capacity under maximum wind conditions of a velocity of 10 ms-1
.
d) the amount of wind electricity in proportion to the total electrical energy required (note this is not
the capacity factor) if there is an average of 8 ms-1 for 5 hours per day, for 300 days a year.
e) the amount of wind electricity in proportion to the total electrical energy required if there is instead
an average of 12 ms-1 over the same time as in part d).
Question 4: (3 points)
An energy entrepreneur is planning a network of pumped sea-water energy storage facilities at
suitable locations around the Australian coast. You can assume each will be a dam with depth of 10 m
and with an average vertical height fall (head) of 150 m applicable to the whole water volume.
Assume the conversion efficiency of the gravitational potential energy (P = m.g.h = mass x acceleration
due to gravity x head) to electrical energy is 90%. The total electrical storage amount to cover is 50
TWh, or approximately 20% of Australia’s total electricity requirement at present.
You may also need g = 9.8 m.s-2 and the density of sea water = 1020 kg.m-3 = 1.02 kg.L-1
.
If the dams are all 1.0 km by 1.0 km in surface area, calculate the number of facilities needed to
meet the total electricity requirement above (to the nearest integer).
You may want to refer to the in-class activity of week 7 for this question.