Climate scientists use the Stefan-Boltzmann Law R=oT4 to estimate the change in the earth's average temperature T (in kelvins) that results from a change in the radiation R (in joules per square meter per second) that the earth receives from the sun. Here, o = 5.67 x 10-8 Js-'m-²K-4. Calculate d R/dt, assuming that T = 283 and 4 = 0.05 K/year. What are the units of dR/dt? %3D dt
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- As the very first rudiment of climatology, estimate the temperature of Earth. Assume it is a perfect sphere and its temperature is uniform. Ignore the greenhouse effect. Thermal radiation from the Sun has an intensity (the "solar constant" S) of about 1370 W/m2 at the radius of Earth's orbit. (a) Assuming the Sun's rays are parallel, what area must S be multiplied by to get the total radiation intercepted by Earth? It will be easiest to answer in tens of Earth's radius, R. (b) Assume that Earth reflects about 30% of the solar energy it intercepts. In other words, Earth has an albedo with a value of A=0.3 . In terms of S, and R, what is the rate at which Earth absorbs energy from the Sun? (c) Find the temperature at which Earth radiates energy at the same rate. Assume that at the infrared wavelengths where it radiates, the emissivity e is 1. Does your result show that the greenhouse effect is important? (d) How does your answer depend on the area of Earth?Answer the following by filling the blank: During a bout with the flu, an 80-kg person ran a fever of 39 oC. Consider that the specific heat of any human body is 3470 J/kg K, how much energy does the body need to burn to reach the fever temperature? The answer (in fundamental SI unit) is ___________ (type the numeric value only, dont use scientific notation)When the coefficient of linear expansion, a, and the temperature change, T-T, are large, a length L, of a solid substance expands in length to a(T, -T₂) L₁ = L₁e O L=L[1 + a(Tƒ– T;)]. ○ Ly=al (Ty-T). O L=L[1 + In(a(T₁-T))]. a(T, I₂ = ₁₂₁[ 1 + ª²(²₁-7)].
- During a bout with the flu an 80-kg person ran a fever of 39 oC. Consider that the specific heat of any human body is 3470 J/kg K, how much energy does the body need to burn to reach the fever temperature? The answer (in fundamental SI unit) is ___________ (type the numeric value only, dont use scientific notation)2.8 At a temperature of 100°C and an absolute pressure of 5 at- mospheres, what is the ratio of the density of water to the den- sity of air, p,/P.?What must be the height of a 200mm diameter vertical pipe carrying hot liquid so that the surrounding area becomes 38degrees C? Note that the rate of convection is 6 KWatts and the surface of the plate is around 90degrees C. answer in meters. (3 decimal places)
- Some amount of heat energy is removed from a 9cm X 26cm X 46cm block of ice to cool from 0ºC to -26ºC. (Hint: to find mass, use the relation between, density, mass and volume) Calculate the following: a) The mas of ice cube in grams (density of ice = 920 kg/m3). b) The temperature difference in kelvin b) The energy removed from ice in calories . (specific heat of ice = 2093 J/kgºC)Compute the energy consumption in units of joules per year, gigawatts (GW), and watts per person as (a) fuel, (b) food, and (c) solar radiation for a country of population density 20 person/km2, an area of 1 million km2, and a fuel energy consumption rate of 250 GJ per person per year. Solar radiation reaching the ground is approximately 150 W/m2. The average person consumes food containing 2000 “calories” per day (1 calorie = 4182 J).Pertaining to Lab 3 Q1 a and b, calculate how much radiation is emitted by the Sun and the Earth (assuming the Sun's average surface temperature is 6000K and the Earth's average temperature is 300K). Please put the entire number that you get as your answer and do not write it in scientific notation.
- Physics Comet C/1995 O1 (Hale-Bopp) has a gas production rate for H2O of Q = 8.35 x 1030 molecules per second at 1.5 AU. Estimate the radius of its nucleus in km. (Use 3 sig. figs.)A bag of frozen vegetables with temperature 32◦F is placed in a 75◦F room. After 20 minutes, the temperature of the vegetables has risen to 41◦F. Using this information, find an exponential formula for the temperature of the vegetables where time is measured in minutes. To find the exponential formula, transform the temperature into a new variable for which the problem can be solved as an exponential growth/decay problem. Then find the formula in that variable and transform back to temperature. Based on the formula, what is the temperature of the vegetables after 45 minutes?A window has dimensions of 1 m by 2.2 m and is made of glass 6.5 mm thick. On a winter day, the outside temperature is 22° C while the inside temperature is a comfortable at 16.5° C. (k of glass =0.175W/m.K) (1.5+1.5+2 = 5marks) Calculate the following: a) the area of the window in square metres b) the tem perature gradient (AT/Ax)in kelvin/metre c) the rate of heat lost through the window by conduction in watts/metre.kelvin