Advertisements
Advertisements
Question
One end of a steel rod (K = 46 J s−1 m−1°C−1) of length 1.0 m is kept in ice at 0°C and the other end is kept in boiling water at 100°C. The area of cross section of the rod is 0.04 cm2. Assuming no heat loss to the atmosphere, find the mass of the ice melting per second. Latent heat of fusion of ice = 3.36 × 105 J kg−1.
Advertisements
Solution
Given:
Thermal conductivity of the rod, K = 46 J s–1 m–1 °C–1
Length of the rod, l = 1 m
Area of the cross-section of the rod, A =0.04 cm2
= 0.04 × 10−4 m2
= 4 × 10−6 m2
Rate of transfer of heat is given by
`(ΔQ)/(Δt) = (ΔT)/ (l/(KA)`
`(ΔQ)/(Δt) = ((T_1 - T_2 ) KA ) / l`
`(ΔQ)/(Δt) =( (100-0 )/1) xx 46 xx 4 xx 10^-6 m^2`
`(DeltaQ)/(Deltat) = 184xx10^-4 J//s`
Also , ΔQ = mL f
`therefore (m/t)L_f = 184 xx 10^-4`
`⇒ ( m/t) xx 3.36 xx 10^5 = 184 xx 10^`
`rArr m=(184xx10^-4)/(3.36xx10^5)xxt`
`rArr m = 5.5xx10^-9xx1 kg//s`
`⇒ m = 5.5 xx 10^-8 xx 10^3 g/s`
`⇒ m = 5.5 xx 10^-5 g/s`
APPEARS IN
RELATED QUESTIONS
Explain why a brass tumbler feels much colder than a wooden tray on a chilly day
A tightly closed metal lid of a glass bottle can be opened more easily if it is put in hot water for some time. Explain.
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.
A steel frame (K = 45 W m−1°C−1) of total length 60 cm and cross sectional area 0.20 cm2, forms three sides of a square. The free ends are maintained at 20°C and 40°C. Find the rate of heat flow through a cross section of the frame.
A cubical box of volume 216 cm3 is made up of 0.1 cm thick wood. The inside is heated electrically by a 100 W heater. It is found that the temperature difference between the inside and the outside surface is 5°C in steady state. Assuming that the entire electrical energy spent appears as heat, find the thermal conductivity of the material of the box.
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.
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.
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.
Following figure shows two adiabatic vessels, each containing a mass m of water at different temperatures. The ends of a metal rod of length L, area of cross section A and thermal conductivity K, are inserted in the water as shown in the figure. Find the time taken for the difference between the temperatures in the vessels to become half of the original value. The specific heat capacity of water is s. Neglect the heat capacity of the rod and the container and any loss of heat to the atmosphere.
A calorimeter of negligible heat capacity contains 100 cc of water at 40°C. The water cools to 35°C in 5 minutes. The water is now replaced by K-oil of equal volume at 40°C. Find the time taken for the temperature to become 35°C under similar conditions. Specific heat capacities of water and K-oil are 4200 J kg−1 K−1 and 2100 J kg−1 K−1respectively. Density of K-oil = 800 kg m−3.
There are two identical vessels filled with equal amounts of ice. The vessels are of different metals. If the ice melts in the two vessels in 20 and 35 minutes respectively, the ratio of the coefficients of thermal conductivity of the two metals is:
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?
Which of the following is a correct example of a bad conductor of heat used in daily life to reduce heat loss or gain?
At the molecular level, how is heat transferred in a solid during conduction?
During conduction along a metal rod, which part becomes hot first, and why?
