Balbharati solutions for Physics [English] 12 Standard HSC Maharashtra State Board chapter 3 - Kinetic Theory of Gases and Radiation [Latest edition]

In an ideal gas, the molecules possess

Choose the correct option.

The mean free path λ of molecules is given by where n is the number of molecules per unit volume and d is the diameter of the molecules. 

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If the pressure of an ideal gas decreases by 10% isothermally, then its volume will ______.

If a = 0.72 and r = 0.24, then the value of t_r is ______.

The ratio of emissive power of perfect blackbody at 1327°C and 527°C is ______.

Answer in brief:

What will happen to the mean square speed of the molecules of a gas if the temperature of the gas increases?

On what factors do the degrees of freedom depend?

Write ideal gas equation for a mass of 7 g of nitrogen gas.

What is an ideal gas?

Does an ideal gas exist in practice?

Define athermanous substance.

Define diathermanous substance.

When a gas is heated, its temperature increases. Explain this phenomenon on the basis of the kinetic theory of gases.

Explain, on the basis of the kinetic theory of gases, how the pressure of a gas changes if its volume is reduced at a constant temperature.

Mention the conditions under which a real gas obeys the ideal gas equation.

State the law of equipartition of energy and hence calculate the molar specific heat of mono-atomic and di-atomic gases at constant volume and constant pressure.

Answer in brief:

What is a perfect blackbody? How can it be realized in practice?

State the Stefan-Boltzmann law.

State the Wien's displacement law

Explain the spectral distribution of blackbody radiation.

Calculate the ratio of the mean square speeds of molecules of a gas at 30 K and 120 K.

Two vessels A and B are filled with the same gas where the volume, temperature, and pressure in vessel A is twice the volume, temperature, and pressure in vessel B. Calculate the ratio of the number of molecules of the gas in vessel A to that in vessel B.

Answer in brief:

A gas in a cylinder is at pressure P. If the masses of all the molecules are made one-third of their original value and their speeds are doubled, then find the resultant pressure.

Answer in brief:

Show that rms velocity of an oxygen molecule is `sqrt2` times that of a sulfur dioxide molecule at S.T.P.

At what temperature will oxygen molecules have same rms speed as helium molecules at S.T.P.? (Molecular masses of oxygen and helium are 32 and 4 respectively).

Answer in brief:

Compare the rms speed of hydrogen molecules at 127ºC with rms speed of oxygen molecules at 27ºC given that molecular masses of hydrogen and oxygen are 2 and 32 respectively.

Find the kinetic energy of 5 litres of a gas at STP, given the standard pressure is 1.013 × 10⁵ N/m².

Calculate the average molecular kinetic energy 

1. per kmol 
2. per kg 
3. per molecule 

of oxygen at 127°C, given that the molecular weight of oxygen is 32, R is 8.31 J mol⁻¹K⁻¹ and Avogadro’s number N_A is 6.02 × 10²³ molecules mol⁻¹.

Calculate the energy radiated in one minute by a blackbody of surface area 100 cm² when it is maintained at 227°C. (Given: σ = 5.67 × 10^-8 W/m².K⁴)

Energy is emitted from a hole in an electric furnace at the rate of 20 W when the temperature of the furnace is 727°C. What is the area of the hole? (Take Stefan’s constant σ to be 5.7 × 10^-8 Js^-1 m^-2K^-4.)

The emissive power of a sphere of area 0.02 m² is 0.5 kcal s^-1m^-2. What is the amount of heat radiated by the spherical surface in 20 seconds?

Compare the rates of emission of heat by a blackbody maintained at 727°C and at 227°C, if the black bodies are surrounded by an enclosure (black) at 27°C. What would be the ratio of their rates of loss of heat?

Earth’s mean temperature can be assumed to be 280 K. How will the curve of blackbody radiation look like for this temperature? Find out λ_max. In which part of the electromagnetic spectrum, does this value lie? (Take Wien's constant b = 2.897 × 10⁻³ m K)

A small blackened solid copper sphere of radius 2.5 cm is placed in an evacuated chamber. The temperature of the chamber is maintained at 100 °C. At what rate must energy be supplied to the copper sphere to maintain its temperature at 110 °C? (Take Stefan’s constant σ to be 5.67 × 10^-8 J s^-1 m^-2 K^-4) and treat the sphere as a blackbody.)

Find the temperature of a blackbody if its spectrum has a peak at (a) λ_max = 700 nm (visible), (b) λ_max = 3 cm (microwave region) (c) λ_max = 3 m (short radio waves). (Take Wien’s constant b = 2.897 × 10^-3 m.K).