Advertisements
Advertisements
प्रश्न
We would like to make a vessel whose volume does not change with temperature (take a hint from the problem above). We can use brass and iron `(β_(vbrass) = (6 xx 10^(–5))/K and β_(viron) = (3.55 xx 10^(–5))/K)` to create a volume of 100 cc. How do you think you can achieve this.
Advertisements
उत्तर
In the previous problem, the difference in the length was constant.
In this problem the difference in volume is constant.
The situation is shown in the diagram.
Let Vio, Vbo be the volume of iron and brass vessel at 0°C
Vi, Vb be the volume of iron and brass vessel at Δθ°C,
γi, γb be the coefficient of volume expansion of iron and brass.
As per the question, Vio – Vbo = 100 cc = Vi – Vb ......(i)
Now, `V_i = V_(io) (1 + γ_iΔθ)`
`V_b = V_(bo) (1 + γ_bΔθ)`
`V_i - V_b = (V_(io) - V_(bo)) + Δθ(V_(io)γ_i - V_(bo)γ_b)`
Since, `V_i - V_b` = constant
So, `V_(io)γ_i - V_(bo)γ_b`
⇒ `V_(io)/V_(bo) = γ_b/γ_i`
= `(3/2 β_b)/(3/2 β_i)`
= `β_b/β_i`
= `(6 xx 10^-5)/(3.55 xx 10^-5)`
= `6/3.55`
`V_(io)/V_(bo) = 6/3.55` ......(ii)
Solving equations (i) and (ii), we get
Vio = 244.9 cc
Vbo = 144.9 cc
APPEARS IN
संबंधित प्रश्न
A child running a temperature of 101°F is given an antipyrin (i.e. a medicine that lowers fever) which causes an increase in the rate of evaporation of sweat from his body. If the fever is brought down to 98 °F in 20 min, what is the average rate of extra evaporation caused, by the drug? Assume the evaporation mechanism to be the only way by which heat is lost. The mass of the child is 30 kg. The specific heat of human body is approximately the same as that of water, and latent heat of evaporation of water at that temperature is about 580 cal g–1.
A geyser heats water flowing at the rate of 3.0 litres per minute from 27 °C to 77 °C. If the geyser operates on a gas burner, what is the rate of consumption of the fuel if its heat of combustion is 4.0 × 104 J/g?
What amount of heat must be supplied to 2.0 x 10-2 kg of nitrogen (at room temperature) to raise its temperature by 45 °C at constant pressure? (Molecular mass of N2 = 28; R = 8.3 J mol-1 K-1.)
A solid of mass 50 g at 150 °C is placed in 100 g of water at 11 °C when the final temperature recorded is 20 °C. Find the specific heat capacity of the solid. (specific heat capacity of water = 4.2 J/g °C)
What do you understand by the following statements:
The specific heat capacity of lead is 130 Jkg-1K-1.
A refrigerator converts 100 g of water at 20°C to ice at -10°C in 35 minutes. Calculate the average rate of heat extraction in terms of watts.
Given: Specific heat capacity of ice = 2.1 J g-1°C-1
Specific heat capacity of water = 4.2 J g-1°C-1
Specific latent heat of fusion of ice = 336 J g-1
50 g of metal piece at 27°C requires 2400 J of heat energy so as to attain a temperature of 327°C . Calculate the specific heat capacity of the metal.
What do you mean by the following statement?
The heat capacity of a body is 50 JK-1?
Water property of water makes it an effective coolant?
The S.I. unit of specific heat capacity is ______.
The specific heat capacity of water is :
Find the time taken by a 500 W heater to raise the temperature of 50 kg of material of specific heat capacity 960 J kg-1K-1, from 18°C to 38° C. Assume that all the heat energy supplied by the heater is given to the material.
Give three reasons for the increase of green house gases.
What is meant by global warming?
State the impact of global warming on life on the earth.
How will climate changes affect the various animal species?
What is meant by specific heat capacity?
How will you prove experimentally that different substances have different specific heat capacities?
What change in heat energy occurs when lead at its melting point
solidifies without change in the temperature?
Name the substance which has maximum specific heat capacity.
Explain, why does a wise farmer water his fields, if forecast is forst?
A piece of ice is heated at a constant rate. The variation of temperature with heat input is shown in the graph below:
(i) What are represented by AB and CD?
(ii) What conclusion can you draw regarding the 110°c nature of ice from the above graph?
The temperature of a lead piece of mass 400 g rises from 20°C to 50°C when 1560 J of heat is supplied to it. Calculate: Heat capacity of lead piece.
A piece of iron of mass 2.0 kg has a thermal capacity of 966 J/°C. What is its specific heat capacity in S.I. units?
The specific heat capacity of water is 1 cal/g °C.
_______ is defined as the amount of heat required to raise the temperature of 1kg of a substance by 1°C.
Define specific heat capacity.
Explain why the specific heat capacity at constant pressure is greater than the specific heat capacity at constant volume.
If 'Cp' and 'Cv' are molar specific heats of an ideal gas at constant pressure and volume respectively. If 'λ' is the ratio of two specific heats and 'R' is universal gas constant then 'Cp' is equal to ______.
Two metals A and B have specific heat capacities in the ratio 2 : 3. If they are supplied the same amount of heat then
Which metal piece will show a greater rise in temperature given their masses is the same?
Two metals A and B have specific heat capacities in the ratio 2:3. If they are supplied same amount of heat then
If the mass ratio of metal A and metal B is 3:5 then calculate the ratio in which their temperatures rise.
Find the odd one out:
A geyser heats water flowing at a rate of 2.0 kg per minute from 30°C to 70°C. If the geyser operates on a gas burner, the rate of combustion of fuel will be ______ g min-1.
[Heat of combustion = 8 × 103 Jg-1 Specific heat of water = 4.2 Jg-1°C-1]
When two kilocalories of heat are supplied to a system, the internal energy of the system increases by 5030 J and the work done by the gas against the external pressure is 3350 J. Calculate J, the mechanical equivalent of heat.
Give one example where high specific heat capacity of water is used as heat reservoir.
