Advertisements
Advertisements
प्रश्न
A rod of negligible heat capacity has length 20 cm, area of cross section 1.0 cm2 and thermal conductivity 200 W m−1°C−1. The temperature of one end is maintained at 0°C and that of the other end is slowly and linearly varied from 0°C to 60°C in 10 minutes. Assuming no loss of heat through the sides, find the total heat transmitted through the rod in these 10 minutes.
Advertisements
उत्तर
Given:
Length of the rod, l = 20 cm = 0.2 m
Area of cross section of the rod, A = 1.0 cm2 = 1.0 × 10 -4m2
Thermal conductivity of the material of the rod, k = 200 W m-1° C-1
The temperature of one end of the rod is increased uniformly by 60° C within 10 minutes.
This mean that the rate of increase of the temperature of one end is 0.1° C per second
`rArr 60/(10xx60)""^circ C//s`
So, total heat flow can be found by adding heat flow every second.
Rate of flow of heat = `(dQ)/dt`
Q"net" = ∑ `(KA)/d ( T_2 - T_1)×Deltat`
For each interval,
`Deltat = 1`
`Q"net" = KA/d ( 0.1 + (KA)/d xx0.2 + (KA)/d xx0.3 + ...................+ KA/dxx 60.0`
`Q"net" = (KA)/d (0.1 + 0.2 +.........+ 60.0)`
sum of n terms of an AP is given by
`s_n = n/2 ( axxa_n)`
`Q_net = (KA)/d xx 600/2 (0.1+60)`
⇒` Q'"net" = (200xx - 10^-4)/(20xx10^-2) xx 600/2xx60.1`
⇒ Qnet = 1800J (approximately)
APPEARS IN
संबंधित प्रश्न
A bullet of mass 20 g enters into a fixed wooden block with a speed of 40 m s−1 and stops in it. Find the change in internal energy during the process.
A block of mass 100 g slides on a rough horizontal surface. If the speed of the block decreases from 10 m s−1 to 5 m s−1, find the thermal energy developed in the process.
One end of a metal rod is kept in a furnace. In steady state, the temperature of the rod
Water is boiled in a container having a bottom of surface area 25 cm2, thickness 1.0 mm and thermal conductivity 50 W m−1°C−1. 100 g of water is converted into steam per minute in the steady state after the boiling starts. Assuming that no heat is lost to the atmosphere, calculate the temperature of the lower surface of the bottom. Latent heat of vaporisation of water = 2.26 × 106 J kg−1.
A pitcher with 1-mm thick porous walls contains 10 kg of water. Water comes to its outer surface and evaporates at the rate of 0.1 g s−1. The surface area of the pitcher (one side) = 200 cm2. The room temperature = 42°C, latent heat of vaporization = 2.27 × 106 J kg−1, and the thermal conductivity of the porous walls = 0.80 J s−1 m−1°C−1. Calculate the temperature of water in the pitcher when it attains a constant value.
The ends of a metre stick are maintained at 100°C and 0°C. One end of a rod is maintained at 25°C. Where should its other end be touched on the metre stick so that there is no heat current in the rod in steady state?
Three rods of lengths 20 cm each and area of cross section 1 cm2 are joined to form a triangle ABC. The conductivities of the rods are KAB = 50 J s−1 m−1°C−1, KBC = 200 J s−1m−1°C−1 and KAC = 400 J s−1 m−1°C−1. The junctions A, B and C are maintained at 40°C, 80°C and 80°C respectively. Find the rate of heat flowing through the rods AB, AC and BC.
A hollow tube has a length l, inner radius R1 and outer radius R2. The material has a thermal conductivity K. Find the heat flowing through the walls of the tube if (a) the flat ends are maintained at temperature T1 and T2 (T2 > T1) (b) the inside of the tube is maintained at temperature T1 and the outside is maintained at T2.
Figure (28-E2) shows a copper rod joined to a steel rod. The rods have equal length and equal cross sectional area. The free end of the copper rod is kept at 0°C and that of the steel rod is kept at 100°C. Find the temperature at the junction of the rods. Conductivity of copper = 390 W m−1°C−1 and that if steel = 46 W m−1°C−1.
An aluminium rod and a copper rod of equal length 1.0 m and cross-sectional area 1 cm2 are welded together as shown in the figure . One end is kept at a temperature of 20°C and the other at 60°C. Calculate the amount of heat taken out per second from the hot end. Thermal conductivity of aluminium = 200 W m−1°C−1 and of copper = 390 W m−1°C−1.
Suppose the bent part of the frame of the previous problem has a thermal conductivity of 780 J s−1 m−1 °C−1 whereas it is 390 J s−1 m−1°C−1 for the straight part. Calculate the ratio of the rate of heat flow through the bent part to the rate of heat flow through the straight part.
The two rods shown in following figure have identical geometrical dimensions. They are in contact with two heat baths at temperatures 100°C and 0°C. The temperature of the junction is 70°C. Find the temperature of the junction if the rods are interchanged.
The three rods shown in figure have identical geometrical dimensions. Heat flows from the hot end at a rate of 40 W in the arrangement (a). Find the rates of heat flow when the rods are joined as in arrangement (b) and in (c). Thermal condcutivities of aluminium and copper are 200 W m−1°C−1 and 400 W m−1°C−1 respectively.
Two bodies of masses m1 and m2 and specific heat capacities s1 and s2 are connected by a rod of length l, cross-sectional area A, thermal conductivity K and negligible heat capacity. The whole system is thermally insulated. At time t = 0, the temperature of the first body is T1 and the temperature of the second body is T2 (T2 > T1). Find the temperature difference between the two bodies at time t.
An amount n (in moles) of a monatomic gas at an initial temperature T0 is enclosed in a cylindrical vessel fitted with a light piston. The surrounding air has a temperature Ts (> T0) and the atmospheric pressure is Pα. Heat may be conducted between the surrounding and the gas through the bottom of the cylinder. The bottom has a surface area A, thickness x and thermal conductivity K. Assuming all changes to be slow, find the distance moved by the piston in time t.
A spherical ball of surface area 20 cm2 absorbs any radiation that falls on it. It is suspended in a closed box maintained at 57°C. (a) Find the amount of radiation falling on the ball per second. (b) Find the net rate of heat flow to or from the ball at an instant when its temperature is 200°C. Stefan constant = 6.0 × 10−8 W m−2 K−4.
