Advertisements
Advertisements
प्रश्न
Calculate the ratio of two specific heats of polyatomic gas molecules.
Advertisements
उत्तर
- Gases that have molecules containing more than two atoms are termed polyatomic gases.
- Each molecule of the polyatomic gas has 3 translational degrees of freedom. Only linear molecules have 2 degrees of freedom for rotation. All other polyatomic molecules have 3 degrees of freedom for rotation.
- The number of degrees of freedom (f) for the vibrational motion of a polyatomic molecule depends on the geometric structure of the molecule, i.e., the arrangement of atoms in a molecule.
- Each such degree of freedom contributes average energy `2 xx 1/2`kBT from kinetic energy and potential energy terms.
- Therefore for 1 mole of a polyatomic gas, the internal energy is E = `3/2 N_Ak_BT + 3/2 N_Ak_BT + f × 2/2 N_Ak_BT`
= (3 + f) NAkBT - Molar-specificific heats at constant volume and constant pressure are given as
Cv = (3 + f) R and Cp = (4 + f) R
∴ `gamma = C_p/C_v = (4 + f)/(3 + f)`
संबंधित प्रश्न
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.)
Water in lakes and ponds do not freeze at once in cold countries. Give a reason is support of your answer.
Heat energy is supplied at a constant rate to 100g of ice at 0 °C. The ice is converted into water at 0° C in 2 minutes. How much time will be required to raise the temperature of water from 0 °C to 20 °C? [Given: sp. heat capacity of water = 4.2 J g-1 °C-1, sp. latent heat of ice = 336 J g-1].
Name the radiations for which the green house gases are transparent ?
Give three reasons for the increase of green house gases.
How will rise in sea level affect population in coastal countries?
What is carbon tax?
Name and state the principle used to measure the specific heat capacity of a substance.
Solve the following problems:
Equal heat is given to two objects A and B of mass 1 g. Temperature of A increases by 3°C and B by 5°C. Which object has more specific heat? And by what factor?
What is the unit of heat capacity in CGS system?
(b) 2000 J of heat energy is required to raise the temperature of 4 kg of a
metal by 3°c. Which expression gives the specific heat capacity of the metal?
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.
A liquid X has specific heat capacity higher than the liquid Y. Which liquid is useful as coolant in car radiators.
Write the approximate values of the specific latent heat of fusion of ice.
Why is specific heat capacity taken as a measure of thermal inertia?
Explain, why water is considered as best liquid for quenching thirst?
Explain, why does a wise farmer water his fields, if forecast is forst?
If substances A and B are liquids then which one would be more useful in car radiators?
Given: Specific heat capacity’A’ 3.8 J/g /K. Specific heat capacity ‘B’ 0.4 J/g /K.
If, in a central heating system, steam enters a radiation pipe at 100°C and water leaves the radiation pipe at 100°C, can this radiation pipe heat a room? Give an explanation for your answer.
The molar specific heat of a gas at constant volume is 12307.69 J kg-1 K-1. If the ratio of the two specific heats is 1.65, calculate the difference between the two molar specific heats of gas.
How much heat energy is necessary to raise the temperature of 5 kg of water from 20°C to 100°C?
Express the change in internal energy in terms of molar specific heat capacity.
The molar specific heats of an ideal gas at constant pressure and constant volume are denoted by Cp and Cv respectively. If `gamma = "C"_"p"/"C"_"v"` and R is the universal gas constant, then Cp is equal to ______.
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?
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.
Match the columns:
| Column ‘A’ | Column ‘B’ |
| The SI unit of specific heat capacity | (a) Jkg−1°C−1 |
| (b) kg/m3 | |
| (c) calorie |
Two blocks P and Q of different metals having their mass in the ratio 2 : 1 are given same amount of heat. Their temperature rises by same amount. Compare their specific heat capacities.
