Advertisements
Advertisements
प्रश्न
Consider the situation shown in the figure . The frame is made of the same material and has a uniform cross-sectional area everywhere. Calculate the amount of heat flowing per second through a cross section of the bent part if the total heat taken out per second from the end at 100°C is 130 J.
Advertisements
उत्तर
`R_{BC} = 1/{KA }= 1/{KA}`
`R_{CD} = 1/{KA }= 60/{KA}`
`R_{CD} = 5/{KA} , R_{AB} = 20/M , R_{EF} = 20/{KA}`
Let ;
`R_1 = R_{BC} + R_{CD} + R_{DE} = 70/{KA}`
Let :
`R_{BE} = 60/{KA} = R_2
q = q1 + q2 ...............(1)
R1 and R2 are in parallel, so total heat across R1 and R2 will be same.
⇒ `q_1R_2 = q_2R_2`
`q_1xx 70/{KA} = q_2xx 60/{KA}`
`7q_1 = 6q_2`
`{7q_1}/{6}= q_2`
From equation (1) and (2),
q = q_1 + {7q_1}/6`
`q = {13q_1}/6`
`q=130 J`
`130 = 13Qq_1`
q1 = 60 J/sec
APPEARS IN
संबंधित प्रश्न
A metal sheet with a circular hole is heated. The hole
Find the ratio of the lengths of an iron rod and an aluminium rod for which the difference in the lengths is independent of temperature. Coefficients of linear expansion of iron and aluminium are 12 × 10–6 °C–1 and 23 × 10–6 °C–1 respectively.
An aluminium plate fixed in a horizontal position has a hole of diameter 2.000 cm. A steel sphere of diameter 2.005 cm rests on this hole. All the lengths refer to a temperature of 10 °C. The temperature of the entire system is slowly increased. At what temperature will the ball fall down? Coefficient of linear expansion of aluminium is 23 × 10–6 °C–1 and that of steel is 11 × 10–6 °C–1.
A glass window is to be fit in an aluminium frame. The temperature on the working day is 40°C and the glass window measures exactly 20 cm × 30 cm. What should be the size of the aluminium frame so that there is no stress on the glass in winter even if the temperature drops to 0°C? Coefficients of linear expansion for glass and aluminium are 9.0 × 10–6 °C–1 and 24 ×100–6°C–1 , respectively.
In a room containing air, heat can go from one place to another
Following Figure shows water in a container having 2.0 mm thick walls made of a material of thermal conductivity 0.50 W m−1°C−1. The container is kept in a melting-ice bath at 0°C. The total surface area in contact with water is 0.05 m2. A wheel is clamped inside the water and is coupled to a block of mass M as shown in the figure. As the block goes down, the wheel rotates. It is found that after some time a steady state is reached in which the block goes down with a constant speed of 10 cm s−1 and the temperature of the water remains constant at 1.0°C. Find the mass M of the block. Assume that the heat flows out of the water only through the walls in contact. Take g = 10 m s−2.
A semicircular rod is joined at its end to a straight rod of the same material and the same cross-sectional area. The straight rod forms a diameter of the other rod. The junctions are maintained at different temperatures. Find the ratio of the heat transferred through a cross section of the semicircular rod to the heat transferred through a cross section of the straight rod in a given time.
Steam at 120°C is continuously passed through a 50 cm long rubber tube of inner and outer radii 1.0 cm and 1.2 cm. The room temperature is 30°C. Calculate the rate of heat flow through the walls of the tube. Thermal conductivity of rubber = 0.15 J s−1 m−1°C−1.
A room has a window fitted with a single 1.0 m × 2.0 m glass of thickness 2 mm. (a) Calculate the rate of heat flow through the closed window when the temperature inside the room is 32°C and the outside is 40°C. (b) The glass is now replaced by two glasspanes, each having a thickness of 1 mm and separated by a distance of 1 mm. Calculate the rate of heat flow under the same conditions of temperature. Thermal conductivity of window glass = 1.0 J s−1 m−1°C−1 and that of air = 0.025 m-1°C-1 .
Four identical rods AB, CD, CF and DE are joined as shown in following figure . The length, cross-sectional area and thermal conductivity of each rod are l, A and K respectively. The ends A, E and F are maintained at temperature T1, T2 and T3 respectively. Assuming no loss of heat to the atmosphere, find the temperature at B.
The coefficient of thermal conductivity depends upon ______.
Heat is associated with ______.
These days people use steel utensils with copper bottom. This is supposed to be good for uniform heating of food. Explain this effect using the fact that copper is the better conductor.
We would like to prepare a scale whose length does not change with temperature. It is proposed to prepare a unit scale of this type whose length remains, say 10 cm. We can use a bimetallic strip made of brass and iron each of different length whose length (both components) would change in such a way that difference between their lengths remain constant. If αiron = 1.2 × 10−5/K and αbrass = 1.8 × 10−5/K, what should we take as length of each strip?
According to Stefan’s law of radiation, a black body radiates energy σT4 from its unit surface area every second where T is the surface temperature of the black body and σ = 5.67 × 10–8 W/m2K4 is known as Stefan’s constant. A nuclear weapon may be thought of as a ball of radius 0.5 m. When detonated, it reaches temperature of 106 K and can be treated as a black body.
- Estimate the power it radiates.
- If surrounding has water at 30°C, how much water can 10% of the energy produced evaporate in 1s? [Sw = 4186.0 J/kg K and Lv = 22.6 × 105 J/kg]
- If all this energy U is in the form of radiation, corresponding momentum is p = U/c. How much momentum per unit time does it impart on unit area at a distance of 1 km?
As per the given figure, two plates A and B of thermal conductivity K and 2 K are joined together to form a compound plate. The thickness of plates are 4.0 cm and 2.5 cm respectively and the area of cross-section is 120 cm2 for each plate. The equivalent thermal conductivity of the compound plate is `(1+5/alpha)`K, then the value of a will be ______.
A cylinder of radius R made of material of thermal conductivity K1 is surrounded by a cylindrical shell of inner radius R and outer radius 3R made of a material of thermal conductivity K2. The two ends of the combined system are maintained at two different temperatures. What is the effective thermal conductivity of the system?
