Imagine that the temperatures within a metal square are as shown by the contour plot below (bottom left): B Contour Plot (blue is low) Vector Field C D Which of the vector plots (on the right) would correctly show the heat flow here? Select one: Select one: O D O B OC O AImagine that the temperature at every location within an object was given by the equation ?" = 290 - - y. The orientation of the axes are shown below: A y GF X C D E RX In what direction is heat flowing at the marked point (C + )? Select one: Select one: O B O A OC O D OE OF OG OHImagine that you are traveling in a train in winter, where temperature inside the train is 23C and outside the temperature is 2C. Every time the train stops at a station, a door opens. 0.5 cubic metres of warm air flows out of the top of the door, and is replaced by 0.5 cubic metres of cold air coming in at the bottom of the door. The density of air is 1.2 kg per cubic metre, and the specific heat capacity of air (at constant pressure) is 1000 J per K per kg. Find out how much thermal energy leaves the train due to this air flow every time the train stops at a station. Enter your answer in KJ. Answer: How much energy (in kilo-joule) do you need to increase the temperature of 50 g water from room temperature (22 C) to boiling point? You may assume that no heat is lost by the water during the heating process. Specific heat capacity of water is 4200 J/K/kg Answer: You are doing experiment using ion irradiation. You fire a beam of ions at a small sample, which has a surface area of one square centimetre (10)"m"). The ion beam heats the sample to a temperature of 500C. The sample is in a vacuum so it will not lose heat by conduction or convection. How much power will the sample radiate? Assume that @ = 5.67 x 10 *Wm K . that absolute zero is-273.15 C, and that the sample is a perfect black body. Enter your answer to at least three significant figures. Answer:Imagine that the temperatures within a metal square are as shown by the contour plot below (bottom left): Contour Plot [blue h low] Vector Fields Which of the vector plots (on the right) would correctly show the heat flow here? Select one: Select one: OA O B OC O D Imagine that it is a hot day and you are thirsty. You get a can of cold drink from the fridge and put it on the table. The can is at a temperature of 4C, and the air around it is at 35C. How rapidly will the can gain heat due to convection? You may assume a surface area of 0.03 cubic metres and a heat transfer coefficient of 5. Enter your answer in Watts, to at least two significant figures. Answer:Imagine that it is a hot day and you are thirsty. You get a can of cold drink from the fridge and put it on the table. The can is at a temperature of 4C, and the air around it is at 35C. How rapidly will the can gain heat due to convection? You may assume a surface area of 0.03 cubic metres and a heat transfer coefficient of 5. Enter your answer in Watts, to at least two significant figures. Answer: Imagine that the temperatures within a metal square are as shown by the contour plot below (bottom left): Contour Plot (blue is low) Vector Fields Which of the vector plots (on the right) would correctly show the heat flow here? Select one: Select one: O O B OA O Fluid flow through pipes is governed by the Hagen-Poiseuille equation (as long as the pipe is narrow and flow fairly slow, so turbulence is avoided). This equation shows that the flow rate () ox R, where R is the radius of the pipe. A particular vein in a heart-attack patient has a radius of 1mm, and is carrying 2 mL of blood per second. A doctor plans to replace this vein with a wider one, with a radius of 3mm. How much blood will flow down this wider vein, everything else being equal? Enter your answer in mL per second. Answer:Water flow through a pipe, if it is fast and turbulent, is governed by the Darcy-Weisbach equation, in which the flow per second () pc D)"/2, where ) is the diameter of the pipe. Imagine that an irrigation scheme if supplied with 10,000 litres per hour, through a pipe of diameter 10cm. If the pipe was replaced with a wider one (diameter 20cm), how many litres per hour could it supply? Answer: The intensity of noise / you hear from a given noise source is inversely proportional to the distance between you and the noise source squared-i.e. I o p-2. The organisers of a music concert are trying to get permission to run the concert in a city park, but neighbors are concerned that it will be too loud. The regulations say that no neighbour should be exposed to sound with pressure waves stronger than 2 Pa (100 dB). The organisers ran a similar concert last year. You measured the noise intensity 300 m from the stage, and found a value of 4Pa. This year, the nearest neighbours will be 400 m from the stage. What intensity of sound (in Pa) will they be exposed to? Answer: If you drop objects of the same size and shape, but different mass, then the terminal velocity at which they fall is proportional to the square root of their mass: i.e.p o vm. Imagine that you drop a tennis ball from a high building and find that its terminal velocity is 20 metres per second. Use scaling to estimate the terminal velocity of a cricket ball. You may assume that it's the same size and shape as a tennis ball. Tennis balls weight around 60g, while cricket balls weigh around 160 g. Enter the velocity to at least two significant figures, in metres per second. Answer: Imagine that you are sitting on a grassy slope. The slope is at an angle of 20 degrees to the horizontal, and you weigh 70 kg. How strong is the normal force which the grass is applying to your bottom? Enter your answer in newtons, and assume g = 9.8 m s-2