Question

PITYSICS 113 - ADVANCHI MITYSICS FOR SCUNTISTS AND INGINKL.SI 1. Thermal questions (1) (ii) What are the three forms of heat transfer? Give the equation for the net rate of heat transfer by radiation and explain all terms used A metal kettle at 100ºC with a surface area of 500 cm is in an environment at a temperature of 25°C. Calculate the net rate of heat transfer to the environment. The emissivity and absorptivity of the kettle is 0.5. (iii) What is the equation which relates the change in length of an object due to thermal expansion, to other parameters? Explain the meaning of all terms used in the equation. How is the coefficient of linear expansion related to the coefficient of areal expansion and the coefficient of volumetric expansion? In a car race some years back, one team tried to avoid stopping for fuel by cooling the fuel down to store more in the steel fuel tank. If they cooled it from 20"C to -10°C, how much more fuel would they store? Neglect the contraction of the tank. Show that the change in the volume of the tank is small compared to the change in volume of the fuel. (iv) Mechanics questions (1) (ii) Show that the horizontal range of a projectile is a maximum for level ground when the angle of projection is 45° Distinguish between an clastic and an inclastic collision, and define what is mcant by a completely inelastic collision. (iii) (iv) State the Principle of the Conservation of Mechanical Energy Two masses in,- 3,5 kg and m2 - 6,0 kg are connected by a string passing over a light frictionless pulley, as shown in the ligure below. The 6.0 kg mass is released from rest a distance of 3,0 m above the floor. Calculate: (a) the speed of each mass just before the 6,0 kg mass hits the floor (b) the additional height the 3,5 kg mass rises after the 6,0 kg mass hits the Noor Wh 6.0 kg 3.5 kg 3.0m

Answer 1

(a) (i) Solano The three forme of heat transfer are (i) Conduction : gt occur when two object at different temperatures are in contact with each other. In this heat flows from the wormer to the cooler object until they both reach at some temperature. (15) Convection 8 et occurs when warmer areas of a liquid or get rise to cooler area in the gas and liquid or get toker cooler liquid or the place of the warmer areas. (T ) Radiation & Radiation in a method of heat transfer that doeß not required any contact between the heat source and the heated object. a) (15) Solerng Meat = grandfer by radiation - be AT" - i da dt is where 6 eminivity stefan-Boltzmann comptant, e is Ait surface area and T in Temperature of hot body,

(a) (11) solun & metal Kettle TK = Surface area of Kettle temperature TH= 100°c 1001 273= 373K A- soo cm² - 500x109 m2 Temperature of enviroment To = 25 c = 25+273 = 298k dQ = Q = be A (T - Te") e = 0.5 (emissivity), 6= 5.67X163 w/ m2 k" Q = 5.67X10-9x0.5 X 3.0x16 2 ( 373" – 2984) Il see = 16.26 Watt Q = 16.26 (6) ůl Soluno Thermal expansion of length- AL= LATLO - i where AL it amount of length increaße or decrease due to temperature increase or decrease , & in linear expension coefficient, to is initial length f obgelt. we can wute final length of object - L- Lo [1+291) — (i) Ana

(6) () Al we know &= linear coefficient (014) - 6) A=22 Area of object we can wüte - ln A= ln 22 ln A = 2 lah derivative with respect to T- Take partial 1 2 4 = 2 + 01 1 da = 24. — ( Similarly for volume copfigent - Val then av = 34. - (1) And int olume