Principles of Physics I PHY-111, Fall'13

PHY 111, Fall'13 Principles of Physics I MLR,MNS,BRACUmlrahman@bracu.ac.bd

Heat and Temperature

Formulus:

Dierent temperature scales are relate byC5 =

F329 =

K273:155

Linear expansion of solid, L = L0T ,where is the coecient of linear expansion

Area expansion, A = A0T , where is thecoecient of area expansion

Volume expansion, V = V0T , where isthe coecient of volume expansion

For isotropic solids, = 2 and = 3 Heart Capacity, = QT ,

Specic Heat, C = Qm T Heat gained or lost by a body of mass m as itundergoes a temperature change T , is givenby Q = mCT

Heat gain by body = Heat lost by body

Quantity of Heat transmitted from face 1 toface 2 in time t,is given by Q = K A(12)tLwhere K is the thermal conductivity of thematerials

By conservation of mass, m = oVo = 1V1

Units(in SI):

Specific heat C = J=kg:oC Thermal conductivity, K = Cal=s:cm:oC =W=m:K

1Cal=s:cm:oC = 418W=m:K 1Cal = 1 kcal = 1000 cal 1 cal=gm:oC = 4184 J=kg:oC

The heat of fusion of water at 0oC is about335 kJ=kg or 80 cal=gm

The heat of vaporization of water at 100oC isabout 2:26MJ=kg or 540 cal=gm

Specific heat of water = 4180 J=kg:oC =1 cal=g:oC

Heat and Temperature M.L.Rahman Page 1 of 3

Principles of Physics I PHY-111, Fall'13

Heat and Temperature !!!!!

Level One

1. At what temperature do the Celsius and Fahrenheit scales coincide? (Ans: 40oC)2. A steel tape is calibrated at 20oC. On a cold day when the temperature is 15oC, what will be the

percentage error in the tape? s = 1:1 105 oC1 (Ans: 0:039)3. Suppose a 60 kg person consumes 2500Cal of food in one day. If the entire heat equivalent of this

food were retained by the person's body, how large a temperature change would it cause? For body,Cbody = 0:83 cal=g

oC, remember that 1Cal = 1 kcal = 1000 cal. (Ans: 50oC)

4. How much heat is required to change 10 gm of ice at exactly 0oC to steam at 100oC (Ans: 7:2 kcal)

5. Determine the temperature that results when 1 kg of ice at exactly 0oC is mixed with 9 kg of waterat 50oC (Ans: 37oC)

6. 10 kg of steam at 100oC is condensed in 500 kg of water at 40oC. What is the resulting temperature?(Ans: 51:8oC)

7. Calculate the quantity of heat required to raise the temperature of a metal block with a heat capacityof 23:1 J=oC by 30oC. (Ans: 693 J)

8. An electric heater supplies 500 J of heat energy to a copper cylinder of mass 32:4 gm. Find theincrease in temperature of the cylinder. Given that specic heat of copper is 385 J=kg oC. (Ans:40:08oC)

9. The opposite faces of a metal plate of 0:2 cm thickness are at a dierence of temperature of 100oC.If the area of the plate is 200 cm2,nd the quantity of heat that will ow through the plate in oneminute. Give that thermal conductivity K = 0:2 CGS unit: (Ans: 12 105 cal)

Level Two

1. A cylinder of diameter 1 cm at 30oC is to be slid into a hole in a steel plate. The hole has a diameter of0:99940 cm at 30oC. To what temperature must the plate be heated? For steel s = 1:1105 oC1(Ans: 57oC)

2. A glass ask is lled to the mark with 20 cm3 of mercury at 18oC. If the ask and its contents areheated to 30oC, how much mercury will be above the mark? Given that g = 9 106 oC1 andm = 182 106 oC1 (Ans: 0:15 cm3)

3. A thermos bottle contains 250 gm of coee at 90oC. To this is added 20 gm of milk at 5oC.Afterequilibrium is established,what is is the temperature of the liquid? Assume that no heat loss to thebottle and Specic heat of coee and milk have the same value of 1 cal=g oC. (Ans: 84oC)

4. A 200 gm copper calorimeter can contains 150 gm of oil at 20oC. To the oil is added 80 gm ofaluminum at 300oC. What will be the temperature of the system after equilibrium is established?Given that specic heat Ccop = 0:093 cal=g

oC, CAl = 0:21 cal=goC and Coil = 0:37 cal=g

oC. (Ans:72oC)

5. A 20 gm piece of aluminium at 90oC is dropped into a cavity in a large block of ice at 0oC. Howmuch ice does the aluminium melt? Give that specic heat of aluminium Cal = 0:21 cal=g

oC. (Ans:4:7 gm)

6. A 3 gm bullet moving at 180m=s enters a bag of sand and stops. By what amount does the tem-peratures of the bullet change if all its KE becomes thermal energy that is added to the bullet? Forbullet Cbullet = 0:0305 cal=g

oC = 128 J=kg oC. (Ans: 127oC)

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Principles of Physics I PHY-111, Fall'13

7. How much heat must be absorbed by ice of mass m = 720 gm at 10oC to take it to liquid state at15oC. If we supply the ice with a total energy of only 210 kJ (as heat), what the are the nal stateand temperature of water? (Ans: Q = 300 kJ; 580 gm water and 140 gm ice at oC)

8. A metal plate 4mm thick has a temperature dierence of 32oC between its faces. Its transmits200 kcal=h through an area of 5 cm2. Calculate the thermal conductivity of this metal in W=m:K.(Ans: 58:5W=m:K)

Level Three

1. The density of gold is 19:30 gm=cm3 at 20oC and the coecient of linear expansion is 14:3 106 oC1. Compute the density of gold at 90oC. (Ans: 19:2 gm=cm3)

2. When a building is constructed at 10oC, a steel beam (cross-sectional area 45 cm2) is put in placewith its ends cemented in pillars. If the sealed ends cannot move, what will be the compressional forcein the beam when the temperature is 25oC. For steel s = 1:1105 oC1 and Y = 21011 N=m2.(Ans: 3:5 105 N)

3. Water is boiled in a rectangular steel tank, the bottom of which is 2 mm thick. If the water level fallsat the rate of 0:01 m in 5 minutes, what is the temperature of lower surface of the tank? Thermalconductivity of steel is 0:012 SI unit and laten heat of steam is 540 kcal=kg (Ans: 103oC)

4. A beverage cooler is in the shape of a cube,42 cm on each inside edge. Its 3 cm thick walls are madeof plastic. When the outside temperature is 20oC, how much ice will melt inside the cooler eachhour? For plastic thermal conductivity Kp = 0:050W=m:k (Ans: 0:38 kg)

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