Advertisements
Advertisements
Question
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
Solution
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
RELATED QUESTIONS
The coolant in a chemical or a nuclear plant (i.e., the liquid used to prevent the different parts of a plant from getting too hot) should have high specific heat.
Calculate the mass of ice needed to cool 150 g of water contained in a calorimeter of mass 50 g at 32 °C such that the final temperature is 5 °C. Specific heat capacity of calorimeter = 0.4 J g-1 °C-1, Specific heat capacity of water = 4.2 J g-1°C-1, latent heat capacity of ice = 330 J g-1.
A copper vessel of mass 100 g contains 150 g of water at 50°C. How much ice is needed to cool it to 5°C?
Given: Specific heat capacity of copper = 0.4 Jg-1 °C-1
The Specific heat capacity of water = 4.2 Jg-1 °C-1
The Specific latent heat of fusion ice = 336 Jg-1
Give one example where high specific heat capacity of water is used as heat reservoir ?
Give three reasons for the increase of green house gases.
What impact will global warming have on the health of the affected population?
What impact will climate changes have on the crops of food?
Without green house effect, the average temperature of earth’s surface would have been:
(a) – 18℃
(b) 33℃
(c) 0℃
(d) 15℃
What change in heat energy occurs when lead at its melting point
solidifies without change in the temperature?
A solid of mass 80 g at 80°C is dropped in 400 g water at 10°C. If final temp. is 30°C, find the sp. heat cap. of the solid.
650 J of heat is required to raise the temp. of 0.25 kg of lead from 15°C to 35°C. Calculate the Sp. heat capacity of lead.
State, with reason, which of the two, boiling water or steam both at 100°C will produce more severe burns.
Fill in the following blank using suitable word:
SI unit of heat is .........
A liquid X has specific heat capacity higher than the liquid Y. Which liquid is useful as coolant in car radiators.
Why is specific heat capacity taken as a measure of thermal inertia?
Explain, why does a wise farmer water his fields, if forecast is forst?
Ice-cream at 0°C feels colder than water at 0°C. Give reason for this observation.
Write an expression for the heat energy liberated by a hot body.
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 Specific heat capacity of lead.
Solve the following problem.
Specific latent heat of vaporization of water is 2.26 × 106 J/kg. Calculate the energy needed to change 5.0 g of water into steam at 100 ºC.
State factors on which the amount of heat radiated by a body depends.
Calculate the ratio of two specific heats of polyatomic gas molecules.
Explain how heat capacity of a solid can be determined by the method of mixture.
The cold object the hot object enclosed in one box of heat-resistant material.
- What changes will occur in the two objects when temperature flows from those objects?
- Which principle can show that the energy exchange takes place between two objects only when kept in isolated system?
Define specific heat capacity.
Two uniform brass rods A and B of length land 2l and radii 2r and r respectively are heated to the same temperature. The ratio of the increase in the volume ofB to that of A is ____________.
A monoatomic gas of pressure 'P' having volume 'V' expands isothermally to a volume '2V' and then adiabatically to a volume '16V'. The final pressure of the gas is ______.
(ratio of specific heats = `5/3`)
Heat is applied to a rigid diatomic gas at constant pressure. The ratio ΔQ : ΔU : ΔW is ______.
The molar specific heat of an ideal gas at constant pressure and constant volume is 'Cp' and 'Cv' respectively. If 'R' is the universal gas constant and the ratio 'Cp' to 'Cv' is 'γ' then CV = ______.
The diagram below shows a cooling curve for 200 g of water. The heat is extracted at the rate of 100 Js-1. Answer the questions that follow:
- Calculate specific heat capacity of water.
- Heat released in the region BC.
Why is water used as a coolant in radiators of a car?
Match the columns:
| Column ‘A’ | Column ‘B’ |
| The SI unit of specific heat capacity | (a) Jkg−1°C−1 |
| (b) kg/m3 | |
| (c) calorie |
Find the odd one out:
Specific heat capacity of a substance X is 1900 Jkg-1°C-1 means ______.
Thermal capacities of substances A and B are same. If mass of A is more than mass of B then:
Which substance will have more specific heat capacity?
