A cylinder of radius `R` made of a material of thermal conductivity `K_(1)` is surrounded by cylindrical shell of inner radius `R` and outer radius `2R` made of a material of thermal con-ductivity `K_(2)` The two ends of the combined system are maintained at two differnet tem-peratures There is no loss of heat across the cylindrical surface and system is in steady state What is the effective thermal conductivity of the system .

A cylinder of radius `R` made of a material of thermal conductivity `K

1.	A cylinder of radius `R` made of a material of thermal conductivity `K_(1)` is surrounded by cylindrical shell of inner radius `R` and outer radius `2R` made of a material of thermal con-ductivity `K_(2)` The two ends of the combined system are maintained at two differnet tem-peratures There is no loss of heat across the cylindrical surface and system is in steady state What is the effective thermal conductivity of the system .
Answer» `A_(1) = pi R^(2) ,A_(2) = pi (4R^(2) -R^(2))` Two cylinders are in parallel `:. K_(eff) (A_(1)+A_(2)) =K_(1) A_(1) +K_(2) A_(2)` `K_(eff) =(K_(1)piR^(2)+K_(2)3piR^(2))/(piR^(2)+3piR^(2)),i.eK_(eff) = ((K_(1)+3K_(2)))/(4)` .

Discussion

No Comment Found

Related InterviewSolutions

Liquid is filled in a vessel which is kept in a room with temperature 20°C. When the temperature of the liquid is 80°C, then it loses heat at the rate of 60 cal/sec. What will be the rate of loss of heat when the temperature of the liquid is 40°C ?A. `180 cal//sec`B. `40 cal // sec`C. `30 cal // sec`D. `20 cal //sec`
The temperature at which a black body of unit area loses its energy at the rate of 1 joule/second isA. `-65^(@)C`B. `65^(@)C`C. 65 KD. None of these
Assertion : The equivalent thermal conductivity of two plates of same thickness in contact (series) is less than the smaller value of thermal conductivity. Reason : For two plates of equal thickness in contact (series) the equivalent thermal conductivity is given by `1/K = 1/K_(1) + 1/K_(2)`A. If both assertion and reason are true and the reason is the correct explanation of the assertion.B. If both assertion and reason are true but reason is not the correct explanation of the assertionC. If assertion is true reason is falseD. If the assertion and reason both are false.
An incandesent light bulb has a tungsten filament that is heated to a temperature `3 xx 106(3)K` when an electric current passes through it If the surface area of the filament is approximately `10^(-4)m m^(2)` and it has an emissivity of `0.3` the power radiated by the bulb is nearly `(sigam = 5.67 xx 10^(-8) W m^(-2) K^(-4))` .A. `138 w`B. `175 w`C. `200 w`D. `225 w`
An incandesent bulb has a thin filament of tungsten that is heated to high temperature by passing an electric current The hot filament emits black-body radiation The filament is observed to break up at random locations after a sufficiently long time of operation due to non-uniform evapo ration of operation due to non-uniform evapo ration of ungsten from the filament If the buld is powered at constant voltage which of the following statement (s) is (are) ture ? .A. The temperature distribution over the filament is uniformB. The resistance over small sections of the filament decreases with timeC. The filament emits more light at higher band of frequencies before it breaks upD. The filament consumes less electrical power to words the end of the life of the bulb
The temperature across two different slabs A and B are shown I the steady state (as shown Fig) The ratio of thermal conductivities of A and B isA. `2:3`B. `3:2`C. `1:1`D. `5:3`
Three metal rods of same lenghs and same area of cross sections having conductivities `1,2,3,` units are connected in series Then their effective conductivity will be .A. 2 unitsB. `1.6` unitsC. `2.4` unitsD. `2.8` units
A slab of stone area `3600 cm^(2)` and thickness `10cm` is exposed on the lower surface to steam at `100^(@)C` A block of ice at `0^(@)C` rest on upper surface of the slab. In one hour `4.8kg` of ice is melted. The thermal conductivity of the stone in `Js^(-1)m^(-1)k^(-1)` is (latent heat of ice `=3.36 xx 10^(5) J//Kg` .A. `12.0`B. `10.5`C. `1.02`D. `1.24`
Two walls of thickness d and d and thermal conductivities k and k are in contact. In the steady state, if the temperature at the outer `T_(1)` and `T_(2)` , the temperature at the common wall isA. `(k_(1)T_(1)d_(2)+k_(2)T_(2)d_(1))/(k_(1)d_(2)+k_(2)d_(1))`B. `(k_(1)T_(1)+k_(2)d_(2))/(d_(1)+d_(2))`C. `((k_(1)d_(1)+k_(2)d_(2))/(T_(1)+T_(2)))T_(1)T_(2)`D. `(k_(1)d_(1)T_(1)+k_(2)d_(2)T_(2))/(k_(1)d_(1)+k_(2)d_(2))`
A hollow sphere of glass whose external and internal radii are `11cm` and `9cm` respec-tively is completely filled with ice at `0^(@)C` and placed in a both of boiling water How long will it take for the ice to melt completely ? Givne that density of ice `=0.9g//cm^(3)` latent heat of fusion of ice `=80 cal//g` and thermal conductivity of glass `=0.002 cal//cm-s^(@)C` .

Discussion

No Comment Found

Related InterviewSolutions

Reply to Comment