A body cools down from 50°C to 45°C in
Question: A body cools down from $50^{\circ} \mathrm{C}$ to $45^{\circ} \mathrm{C}$ in 5 minutes and to $40^{\circ} \mathrm{C}$ in another 8 minutes. Find the temperature of the surrounding. Solution:...
Read More →Differentiate each of the following w.r.t
Question: Differentiate each of the following w.r.t $x$ : $\tan ^{-1}\left\{\frac{\sqrt{x}-x}{1+x^{3 / 2}}\right\}$ Solution:...
Read More →A calorimeter of negligible heat capacity contains
Question: A calorimeter of negligible heat capacity contains $100 \mathrm{cc}$ of water at $40^{\circ} \mathrm{C}$. The water cools to $35^{\circ} \mathrm{C}$ in 5 minutes. The water is now replaced by K-oil of equal volume at $40^{\circ} \mathrm{C}$ Find the time taken for the temperature to become $35^{\circ} \mathrm{C}$ under similar conditions. Specific heat capacities of water and K-oil are $4200 \mathrm{~J} / \mathrm{kg}$ - $\mathrm{K}$ and $2100 \mathrm{~J} / \mathrm{kg}-\mathrm{K}$ respe...
Read More →One end of a rod of length 20cm is inserted in a furnace at 800K.
Question: One end of a rod of length $20 \mathrm{~cm}$ is inserted in a furnace at $800 \mathrm{~K}$. The sides of the rod are covered with an insulating material and the other end emits radiation like a blackbody. The temperature of this end is $750 \mathrm{~K}$ in the steady state. The temperature of the surrounding air is $300 \mathrm{~K}$. Assuming radiation to be the only important mode of energy transfer between the surrounding and the open end of the rod, find the thermal conductivity of ...
Read More →Differentiate each of the following w.r.t
Question: Differentiate each of the following w.r.t $x$ : $\tan ^{-1}\left(\frac{a-x}{1+a x}\right)$ Solution:...
Read More →A cylindrical rod of length 50 cm and cross - sectional
Question: A cylindrical rod of length $50 \mathrm{~cm}$ and cross - sectional area $1 \mathrm{~cm}^{2}$ is fitted between a large ice chamber at $0^{\circ} \mathrm{C}$ and an evacuated chamber maintained at $27^{\circ} \mathrm{C}$ as shown in figure. Only small portions of the rod are inside the chambers and the rest is thermally insulated from the surrounding. The cross - section going into the evacuated chamber is blackened so that it completely absorbs any radiation falling on it. The tempera...
Read More →A spherical ball A of surface area 20cm squer is kept at the centre of
Question: A spherical ball A of surface area $20 \mathrm{~cm}^{2}$ is kept at the centre of a hollow spherical shell B of area $80 \mathrm{~cm}^{2}$. The surface of $A$ and the inner surface of $B$ emit as blackbodies. Assume that the thermal conductivity of the material of $B$ is very poor and that of $A$ is very high and that the air between $A$ and $B$ has been pumped out. The heat capacities of $\mathrm{A}$ and $\mathrm{B}$ are $42 \mathrm{~J} /{ }^{\circ} \mathrm{C}$ and $82 \mathrm{~J} /{ ...
Read More →A copper sphere is suspended in an evacuated chamber maintained at
Question: A copper sphere is suspended in an evacuated chamber maintained at $300 \mathrm{~K}$. The sphere is maintained at a constant temperature of $500 \mathrm{~K}$ by heating it electrically. A total of $210 \mathrm{~W}$ of electric power is needed to do it. When the surface of the copper sphere is completely blackened, $700 \mathrm{~W}$ is needed to maintain the same temperature of the sphere. Calculate the emissivity of copper. Solution:...
Read More →A cubical block of mass 1.0 kg and edge 5.0 cm
Question: A cubical block of mass $1.0 \mathrm{~kg}$ and edge $5.0 \mathrm{~cm}$ is heated to $227^{\circ} \mathrm{C}$ it is kept in an evacuated chamber maintained at $27^{\circ} \mathrm{C}$ Assuming that the block emits radiation like a blackbody, find the rate at which the temperature of the block will decrease. Specific heat capacity of the material of the block is $400 \mathrm{~J} / \mathrm{kg}-\mathrm{K}$. Solution:...
Read More →A spherical tungsten piece of radius 1.0cm
Question: A spherical tungsten piece of radius $1.0 \mathrm{~cm}$ is suspended in an evacuated chamber maintained at $300 \mathrm{~K}$. The piece is maintained at $1000 \mathrm{~K}$ by heating it electrically. Find the rate at which the electrical energy must be supplied. The emissivity of tungsten is $0.30$ and the Stefan constant $\sigma$ is $6.0 \times 10^{-8} W / m^{2}-K^{4}$. Solution:...
Read More →A spherical ball of surface area
Question: A spherical ball of surface area $20 \mathrm{~cm}^{2}$ absorbs any radiation that falls on it. It is suspended in a closed box maintained at $57^{\circ} \mathrm{C}$. (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 $200^{\circ} \mathrm{C}$. Stefan constant $=6.0 \times 10^{-8} \mathrm{~W} / \mathrm{m}^{2}-K^{4}$ Solution:...
Read More →A 100 W bulb has tungsten filament of length
Question: A $100 \mathrm{~W}$ bulb has tungsten filament of length $1.0 \mathrm{~m}$ and radius $4 \times 10^{-5} \mathrm{~m}$. The emissivity of the filament is $0.8$ and $\sigma=6.0 \times 10^{-8} W / m^{2}-K^{4}$. Calculate the temperature of the filament when the bulb is operating at correct wattage. Solution:...
Read More →Differentiate each of the following w.r.t
Question: Differentiate each of the following w.r.t $x$ : $\cos ^{-1}(2 x)+2 \cos ^{-1} \sqrt{1-4 x^{2}}$ Solution:...
Read More →A solid aluminium sphere and a solid copper sphere of twice the radius
Question: A solid aluminium sphere and a solid copper sphere of twice the radius are heated to the same temperature and are allowed to cool under identical surrounding temperatures. Assume that the emissivity of both the spheres is the same. Find the ratio of (a) the rate of heat loss from the aluminium sphere to the rate of heat loss from the copper sphere and (b) the rate of fall of temperature of the aluminium sphere to the rate of fall of temperature of the copper sphere. The specific heat c...
Read More →Calculate the amount of heat radiated per second by
Question: Calculate the amount of heat radiated per second by a body of surface area $12 \mathrm{~cm}^{2}$ kept in thermal equilibrium in a room at temperature $20^{\circ} \mathrm{C}$. The emissivity of the surface $=0.80$ and $\sigma=6.0 \times 10^{-8} W / m^{2}-K^{4}$ Solution:...
Read More →Assume that the total surface area of a human body is
Question: Assume that the total surface area of a human body is $1.6 \mathrm{~cm}^{2}$ and that it radiates like an ideal radiator. Calculate the amount of energy radiated per second by the body if the body temperature is $37^{\circ} \mathrm{C}$. Stefan constant $\sigma$ is $6.0 \times 10^{-8} \mathrm{~W} / \mathrm{m}^{2}-\mathrm{K}^{4}$. Solution:...
Read More →Differentiate each of the following w.r.t
Question: Differentiate each of the following w.r.t $x$ : $\tan ^{-1}\left\{\frac{e^{2 x}+1}{e^{2 x}-1}\right\}$ Solution:...
Read More →An amount n (in moles) of a monatomic gas at an initial temperature
Question: An amount $n$ (in moles) of a monatomic gas at an initial temperature $T_{0}$ is enclosed in a cylindrical vessel fitted with a light piston. The surrounding air has a temperature $T_{s}\left(T_{0}\right)$ and the atmospheric pressure is $p_{a}$. 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 i...
Read More →Two bodies of masses m1 and m2 specific heat capacities s1 and s2
Question: Two bodies of masses $m_{1}$ and $m_{2}$ and specific heat capacities $s_{1}$ and $s_{2}$ are connected by a rod of thermally insulated. At time $t=0$, the temperature of the first body is $T_{1}$ and the temperature of the second body is $T_{2}\left(T_{2}T_{1}\right)$ Find the temperature difference between the two bodies at time $t$. Solution:...
Read More →Differentiate each of the following w.r.t
Question: Differentiate each of the following w.r.t $x$ : $\sin ^{-1}\left\{\frac{x^{2}}{\sqrt{x^{4}+a^{4}}}\right\}$ Solution:...
Read More →Figure shows two adiabatic vessels, each containing a mass
Question: Figure shows two adiabatic vessels, each containing a mass $m$ of water at different temperatures. The ends of a metal rod of length $\mathrm{L}$, area of cross - section $\mathrm{A}$ and thermal conductivity $\mathrm{K}$, 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 a...
Read More →A hollow metallic sphere of radius 20cm surrounds
Question: A hollow metallic sphere of radius $20 \mathrm{~cm}$ surrounds a concentric metallic sphere of radius $5 \mathrm{~cm}$. The space between the two spheres is filled with a nonmetallic material. The inner and outer spheres are maintained at $50^{\circ} \mathrm{C}$ and $10^{\circ} \mathrm{C}$ respectively and it is found that $100 \mathrm{~J}$ of heat passes from the inner sphere to the outer sphere per second. Find the thermal conductivity of the material between the spheres. Solution:...
Read More →Differentiate each of the following w.r.t
Question: Differentiate each of the following w.r.t $x$ : $\tan ^{-1}\left\{\frac{\sqrt{1+a^{2} x^{2}}-1}{a x}\right\}$ Solution:...
Read More →A rod of negligible heat capacity has length
Question: A rod of negligible heat capacity has length $20 \mathrm{~cm}$, area of cross - section $1.0 \mathrm{~cm}^{2}$ and thermal conductivity $200 \mathrm{~W} / \mathrm{m}-{ }^{\circ} \mathrm{C}$ The temperature of one end is maintained at $0^{\circ} \mathrm{C}$ and that of the other end is slowly and linearly varied from $0^{\circ} \mathrm{C}$ to $60^{\circ} \mathrm{C}$ in 10 minutes. Assuming no loss of heat through the sides, find the total heat transmitted through the rod in these 10 min...
Read More →Find the rate of heat flow through a cross - section of the rod
Question: Find the rate of heat flow through a cross - section of the rod shown in figure $\left(\theta_{2}\theta_{1}\right)$ Thermal conductivity of the material of the rod is $\mathrm{K}$. Solution:...
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