Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Given:
Volume of water, V = 100 cc = 100×10-3 m3
Change in the temperature of the liquid, ∆θ = 5°C
Time, T = 5 min
For water,
`(msDelta theta)/t =(KA)/l(T_1- T_0 )`
`⇒ (ms)/t = (KA)/l ((T_1-T_0))/(Deltatheta)`
⇒`(100xx10^-3xx1000xx4200)/5 =( KA)/(l) ((313 - T_0))/(Deltatheta)`.........(i)
For K-oil,
`(ms)/t = (KA)/(l)(9(T_1 - T_0))/(Deltatheta)`
⇒ `(ms)/t=(KA)/(l)((T_1 - T_0))/(Deltatheta) `
⇒ `(Vps)/t = (KA)/(l)(T_1 - T_0)/(Deltatheta)`
`⇒ (100xx10^-3xx800xx2100)/(t) = (KA)/(l)((313-T_0))/(Deltatheta)` .............(ii)
From (i) and (ii),
`(100xx10^_3xx800xx2100)/(t) = (100xx10^-5xx1000xx4200)/5`
⇒ t = `(5xx800xx2100)/(1000xx4200) = (2000)/1000`
⇒ t = 2 min
APPEARS IN
संबंधित प्रश्न
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.
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.
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.
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.
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.
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.
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?
A thin rod having length L0 at 0°C and coefficient of linear expansion α has its two ends maintained at temperatures θ1 and θ2, respectively. Find its new length.
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?
In conduction, how does heat mainly travel through a solid rod kept with one end in a flame?
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?
