Advertisements
Advertisements
प्रश्न
Water at 50°C is filled in a closed cylindrical vessel of height 10 cm and cross sectional area 10 cm2. The walls of the vessel are adiabatic but the flat parts are made of 1-mm thick aluminium (K = 200 J s−1 m−1°C−1). Assume that the outside temperature is 20°C. The density of water is 100 kg m−3, and the specific heat capacity of water = 4200 J k−1g °C−1. Estimate the time taken for the temperature of fall by 1.0 °C. Make any simplifying assumptions you need but specify them.
उत्तर
Area of cross section, A = 10 cm2 = 10 × 10–4 m2
Thermal conductivity, K = 200 Js–1 m–1 °C–1
Height, H = 10 cm
Length, l = 1 mm =10–3 m
Temperature inside the cylindrical vessel, T1 = 50°C
temperature outside the vessel, T2 = 30°C
Rate of flow of heat from 1 flat surface will be given by
`(DeltaQ)/(Deltat) = (T_1 -T_2)/( l /(KA)`
`(DeltaQ)/(Deltat) = ((50 - 30 ) xx 200 xx 10^-3)/ 10^-3`
`(DeltaQ)/(Deltat)` = 6000 J/s
Heat escapes out from both the flat surfaces.
Net rate of heat flow = 2 × 6000 = 12000 J/sec
`(DeltaQ)/(Deltat) = (m.s.DeltaT)/ (Deltat)`
Mass = Volume density
`⇒10^-3 xx 0.1 xx 1000 =0.1g`
Using this in the above formula for finding the rate of flow of heat, we get
`12000 = 0.1 xx 4200 xx (DeltaT)/(t)`
`⇒ (DeltaT)/(Deltat) = 12000/420 = 28.57 `
As `DeltaT = 1^circ C`
⇒ `1/t = 28.57`
⇒ `t = 1/28.57 = 0.035 sec`
APPEARS IN
संबंधित प्रश्न
A van of mass 1500 kg travelling at a speed of 54 km h−1 is stopped in 10 s. Assuming that all the mechanical energy lost appears as thermal energy in the brake mechanism, find the average rate of production of thermal energy is cal s−1.
The thermal conductivity of a rod depends on
A hot liquid is kept in a big room. The logarithm of the numerical value of the temperature difference between the liquid and the room is plotted against time. The plot will be very nearly
A piece of charcoal and a piece of shining steel of the same surface area are kept for a long time in an open lawn in bright sun.
(a) The steel will absorb more heat than the charcoal
(b) The temperature of the steel will be higher than that of the charcoal
(c) If both are picked up by bare hand, the steel will be felt hotter than the charcoal
(d) If the two are picked up from the lawn and kept in a cold chamber, the charcoal will lose heat at a faster rate than the steel.
A uniform slab of dimension 10 cm × 10 cm × 1 cm is kept between two heat reservoirs at temperatures 10°C and 90°C. The larger surface areas touch the reservoirs. The thermal conductivity of the material is 0.80 W m−1 °C−1. Find the amount of heat flowing through the slab per minute.
A icebox almost completely filled with ice at 0°C is dipped into a large volume of water at 20°C. The box has walls of surface area 2400 cm2, thickness 2.0 mm and thermal conductivity 0.06 W m−1°C−1. Calculate the rate at which the ice melts in the box. Latent heat of fusion of ice = 3.4 × 105 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?
A hole of radius r1 is made centrally in a uniform circular disc of thickness d and radius r2. The inner surface (a cylinder a length d and radius r1) is maintained at a temperature θ1 and the outer surface (a cylinder of length d and radius r2) is maintained at a temperature θ2 (θ1 > θ2). The thermal conductivity of the material of the disc is K. Calculate the heat flowing per unit time through the disc.
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.
Following Figure shows an aluminium rod joined to a copper rod. Each of the rods has a length of 20 cm and area of cross section 0.20 cm2. The junction is maintained at a constant temperature 40°C and the two ends are maintained at 80°C. Calculate the amount of heat taken out from the cold junction in one minute after the steady state is reached. The conductivites are KAt = 200 W m−1°C−1 and KCu = 400 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 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.
Seven rods A, B, C, D, E, F and G are joined as shown in the figure. All the rods have equal cross-sectional area A and length l. The thermal conductivities of the rods are KA = KC = K0, KB = KD = 2K0, KE = 3K0, KF = 4K0 and KG = 5K0. The rod E is kept at a constant temperature T1 and the rod G is kept at a constant temperature T2 (T2 > T1). (a) Show that the rod F has a uniform temperature T = (T1 + 2T2)/3. (b) Find the rate of heat flowing from the source which maintains the temperature T2.
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.
A hollow metallic sphere of radius 20 cm surrounds a concentric metallic sphere of radius 5 cm. The space between the two spheres is filled with a nonmetallic material. The inner and outer spheres are maintained at 50°C and 10°C respectively and it is found that 100 J of heat passes from the inner sphere to the outer sphere per second. Find the thermal conductivity of the material between the spheres.
