Closed Book. The time allowed for Part A plus Part B in total is 75 minutes.

Transcription

1 1 -Test 1 Closed Book. The time allowed for Part A plus Part B in total is 75 minutes. Answers are to be written on the answer sheets given (one sheet for Part A and another for Part B). PART A 1. Lake Ontario has a volume of 1,640 km 3. What volume of gasoline would need to be burned (assuming 35% combustion efficiency) to heat it up by 1 o C? Gasoline contains 35 MJ of energy per litre. (a) 5.62x10 11 litres (b) 6.88x10 10 litres (c) 1.28x10 11 litres (d) 1.97x10 11 litres 2. Earth s angle of obliquity is 23.5 o off the plane of the ecliptic. If an asteroid hits Earth and we are knocked to a new angle of 30 o, which of the following will occur? (a) Winter time will be longer in the northern hemisphere (b) The pole star will no longer point north in the northern hemisphere (c) The annual amount of energy reaching the Earth from the sun will change (d) The equator will move further north 3. From the deck of a cruise ship, which is 50m above sea level, a 2m tall person watches the palm tree on a desert island slowly disappear over the horizon. How far away will the ship be when the treetop, which is 15m above sea level at the top, disappears from view? (a) 25.7 km (b) 29.2 km (c) km (d) 14.7 km 4. The southern hemisphere has a greater percentage of its surface covered in ocean when compared to the northern hemisphere. What is the impact on the southern hemisphere s average summer temperature? (a) It is cooler than in the northern hemisphere summer (b) It is warmer than in the northern hemisphere summer (c) None as the Earth is closest to the sun during the southern hemisphere summer (d) None as the Earth is furthest from the sun during the southern hemisphere summer 5. Imagine that today was November 30 th. Where would the sun rise on the horizon from a location with a latitude of 20 o N? (a) Due east (b) North of due east (c) South of due east (d) Due south ANS C

2 2 6. A distant star of radius 100 million km has a surface temperature of 3,000K. What is the energy output per second per km 2 of surface area? The Stefan Boltzmann constant, σ = 5.67x10-8 Wm 2 K 4 (a) 4.59x10 6 J (b) 1.84x10 29 J (c) 1.84x10 23 J (d) 4.59x10 12 J 7. What is the maximum angle of elevation of the sun above the horizon (its zenith) at midday in Toronto, (latitude 43.5ºN) on December 21 st, the southern hemisphere mid summer s day? (a) 46.5º (b) 43.5º (c) 23º (d) 66.5º ANS C 8. A Mars Bar (a type of chocolate bar) contains 964 kj of energy. A typical lecture theatre has dimensions of 10 m x 30 m x 5 m. A student eats the Mars Bar then stays in the theatre all day. Assuming 100% of the chocolate bar s energy is put into heating the room, calculate the temperature rise in the room. (a) 0.5 o C (b) o C (c) o C (d) 0.01 o C 9. Jupiter has the largest gravitational impact on the solar system after the sun. If you were able to stand on its surface, what acceleration due to gravity, g, would you experience if you had a mass of 70 kg? The mass of Jupiter is 1.9 x kg and its radius is 69,900 km. The gravitational constant, G is Nm 2 kg 2. (a) 1,815 N (b) 25.9 ms -2 (c) 6.48 ms -2 (d) 1.6 ms The perihelion of a planet occurs: (a) Exactly at the point in time in between its two equinoxes (b) At its furthest point from the star it orbits (c) On the shortest day of the year (d) At its closest point to the star it orbits 11. At a certain depth in the ocean, which of the following is possible? (a) That water of two different temperatures is present in adjacent water columns (b) That water of two different salinities is present in adjacent water columns (c) That water with different salinity AND temperature is present in adjacent water columns (d) All of these answers are possible

3 3 12. The sun sets for good on December 1 st in Cambridge Bay, Nunavut due to its high latitude. The ground is frozen to a depth of 30 cm on that day. The average moisture content the first meter of soil is 30% by mass AND volume, with the rest made of various solid materials. The mixture has a combined thermal conductivity of 1 Wm -1 K -1. If the average temperature for December is -20 o C, how deep will the frost line be on January 1 st? The density of ice is 916 kgm -3. Ignore any ground temperature drop below 0 o C in your calculations. (a) 2.25 m (b) 58 cm (c) 1.95 m (d) 88 cm 13. Night temperatures in desert regions can fall to surprisingly low levels and frosts may occur. The most likely reason for this is: (a) Surfaces that heat quickly will also cool more quickly (b) The high albedo of desert surfaces (c) A lack of ground moisture (d) A lack of cloud cover at night allows the ground and thus the air to cool quickly due to radiant losses 14. Where is the moon during a new moon? (a) Between the Earth and the sun (b) Behind the Earth from the sun (c) Directly in the Earth s shadow from the sun (d) At 90 to the Earth from the sun

4 4 PART B 1. Kiehl and Trenberth (1997) generated this amazingly comprehensive graphic showing what happens to the sun s energy on average when it reaches Earth. The Stefan Boltzmann constant, σ = 5.67x10-8 Wm 2 K 4 (8 marks total)! i) Calculate the average albedo of the Earth (1 mark) For the Earth as a whole, albedo (reflectance) = 107/ (342) = 0.31 ii) Calculate the Earth s average surface temperature in degrees Celsius (2 marks) Use the Stefan Boltzmann equation and the 390 W/m 2 surface radiation number, E = σt = 5.67x10-8 T 4 T = 288K = 15 o C iii) Calculate the total annual energy per m 2 of surface area leading to evaporation of water from the surface. (1 marks) 78W/m 2 contributes to evapo-transpiration Annual that means Q = 78W x 3,600 seconds/hr x 24 hr/day x 365 days/year Total energy intensity = 2.46 x 10 9 J/m 2 iv) Then calculate the total annual rainfall on Earth in litres (2 marks) Total energy contribution = 2.46 x 10 9 J/m 2 x SA of Earth = 2.46 x 10 9 J/m 2 x 4 πr 2 = 2.46 x 10 9 x 4 π x (6,375,000) 2

5 5 = x J Now Q=mL where m = volume of rain, L = typical energy required to evaporate water x = m x 2.5x10 6 m = 5.0 x litres Note: can split problem into two parts using Q = mct with average temperature from (ii) above, then latent heat of evaporation of 2.26x10 6 J/kg v) How many meters of rain is this on average per m 2 of surface area annually? (2 marks) Average = total rainfall / SA = 5.0 x litres / 4 πr 2 = 5.0 x litres / 4 π6,375,000 2 = 979 litres per m 2 = 0.98 meters of rain Can also reach answer by going straight from answer to (iii) above 2. On a sunny winter s day, an average of 600 Wm -2 falls onto the horizontal plane over a 5-hour period. It strikes a pond whose frozen surface is at the point of melting and has a temperature of 0 o C. (5 marks total) i) If the ice has an albedo 0.8 and a depth of 20 cm, calculate the mass of ice per m 2 that will melt during the 5-hour period. The density of ice is 916 kgm -3 (2 marks) 600 W/m 2 x (100%-80%) = 120 W/m 2 across the ice surface Over 5 hours, total energy = 120 x 5 hrs x 60 mins x 60 seconds = 2.16 MJ Ice that will melt, m = Q/L = 2.16 MJ / 334,000 = 6.47 kg per m 2 of surface area ii) If the ice were 5 cm deep, would the ice surface totally disappear by the end of that 5- hour time period? (1 mark) Density of ice = 916 kg/m kg represents 6.4/916 = 0.7% of the total equivalent of 1m 3 of ice, or a depth of 0.7mm. With a total of 5cm of ice present, the ice will still remain at the end of the day iii) One month later, all the ice has melted and the average solar intensity has increased to 800 Wm -2. The water now absorbs 100% of the energy. If 10% of that energy results in surface evaporation, what mass of water is evaporated per hour if the lake is 10km x 20 km in size? (2 mark) 80 W/m2 x 10,000 m x 20,000 m x60 mins x 60 secs = 5.76x10 13 J Q=mL so m = 5.76x10 13 J / 2.5 MJ/litre = 2.3 x 10 7 litres (or kg)