Advertisements
Advertisements
प्रश्न
Show that for monoatomic gas the ratio of the two specific heats is 5:3.
Advertisements
उत्तर
- For a monatomic gas enclosed in a container, held at a constant temperature T, and containing NA atoms, each atom has only 3 translational degrees of freedom.
- Therefore, the average energy per atom is `3/2` kBT and the total internal energy per mole is, E = `3/2` NAkBT
- Molar specific heat at constant volume
Cv = `"dE"/"dT" = 3/2"N"_"A""k"_"B" = 3/2"R"` - Using Mayer’s relation, CP = R + CV
∴ Cp = `5/2`R
∴ `"C"_"p"/"C"_"v" = 5/3`
APPEARS IN
संबंधित प्रश्न
Estimate the total number of air molecules (inclusive of oxygen, nitrogen, water vapour and other constituents) in a room of capacity 25.0 m3 at a temperature of 27 °C and 1 atm pressure
Estimate the average thermal energy of a helium atom at the temperature of 10 million Kelvin (the typical core temperature in the case of a star).
At what temperature is the root mean square speed of an atom in an argon gas cylinder equal to the rms speed of a helium gas atom at – 20 °C? (atomic mass of Ar = 39.9 u, of He = 4.0 u).
50 m3 of saturated vapour is cooled down from 30°C to 20°C. Find the mass of the water condensed. The absolute humidity of saturated water vapour is 30 g m−3 at 30°C and 16 g m−3 at 20°C.
What do you understand by gas?
What is diffusion? Give an example to illustrate it.
Match the following:
|
|
Column A |
Column B |
|
(a) |
cm3 |
(i) Pressure |
|
(b) |
Kelvin |
(ii) Temperature |
|
(c) |
Torr |
(iii) Volume |
|
(d) |
Boyle's law |
(iv) `"V"/"T" = ("V"_1)/("T"_1)` |
|
(a) |
Charles's law |
(v) `"PV"/"T" = ("P"_1 "V"_1)/"T"_1` |
|
|
|
(vi) PV = P1V1 |
A gas occupies 500 cm3 at a normal temperature. At what temperature will the volume of the gas be reduced by 20% of its original volume, the pressure is constant?
Correct the following statement:
0°C is equal to zero Kelvin.
Name or state the following:
The standard pressure of a gas in cm. of mercury corresponding to one atmospheric pressure.
The average energy per molecule is proportional to ______
If the absolute temperature of a body is doubled, the power radiated will increase by a factor of ______
Show that for diatomic gas the ratio of the two specific heats is 7:5.
Gases exert pressure on the walls of the container because the gas molecules ______
The equation of state for 2g of oxygen at a pressure 'P' and temperature 'T', when occupying a volume 'V' will be ______.
Estimate the average thermal energy of a helium atom at room temperature (27 °C).
At room temperature, a diatomic gas is found to have an r.m.s. speed of 1930 ms-1. The gas is ______.
For a wave, y = 0.0002 sin`[2pi(110"t"-x/3)+pi/3]` is travelling in a medium. The energy per unit volume being transferred by wave if density of medium is 1.5 kg/m3, is ______.
P ∝ T at constant volume is the statement of ______.
Two tanks of equal volume contain equal mass of oxygen and nitrogen at 127°C. Find the ratio of pressure in two tanks.
