Advertisements
Advertisements
प्रश्न
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).
Advertisements
उत्तर १
Temperature of the helium atom, THe = –20°C= 253 K
Atomic mass of argon, MAr = 39.9 u
Atomic mass of helium, MHe = 4.0 u
Let, (vrms)Ar be the rms speed of argon.
Let (vrms)He be the rms speed of helium.
The rms speed of argon is given by:
`(v_"rms")_"Ar" = sqrt((3RT_"Ar")/M_"Ar")` .... (1)
Where,
R is the universal gas constant
TAr is temperature of argon gas
The rms speed of helium is given by:
`(v_"rms")_"He" = sqrt((3RT_"He")/M_"He")` ... (ii)
It is given that
(vrms)Ar = (vrms)He
`sqrt((3RT_"Ar")/ M_"Ar")` = `sqrt((3RT_"He")/M_"He")`
`T_"Ar"/M_"Ar" = T_"He"/M_"He"`
`T_"Ar" = T_"He"/M_"He" xx M_"Ar"`
`= 253/4 xx 39.9`
= 2523.675 = 2.52 × 103 K
Therefore, the temperature of the argon atom is 2.52 × 103 K.
उत्तर २
Let C and C’ be the rms velocity of argon and a helium gas atoms at temperature T K and T K respectively
Here, M = 39.9; M’ = 4.0; T =?; T = -20 + 273 = 253 K
Now, `C = sqrt((3RT)/M
)= sqrt((3RT)/39.9)` and `C' = sqrt((3RT')/M') = sqrt(3R xx 253)/4`
Since C =C'
Therefore `sqrt((3RT)/39.9) = sqrt(3Rxx253)/4` or `T = (39.9 xx 253)/4 = 2523.7 K`
संबंधित प्रश्न
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?
During the practical session in the lab when hydrogen sulphide gas having offensive odour is prepared for some test, we can smell the gas even 50 metres away. Explain the phenomenon.
What is diffusion? Give an example to illustrate it.
Choose the correct answer:
The graph of PV vs P for gas is
Correct the following statement:
0°C is equal to zero Kelvin.
Name or state the following:
An equation used in chemical calculations which gives a simultaneous effect of changes of temperature and pressure on the volume of a given mass of dry gas
Name or state the following:
The absolute temperature value corresponding to 35°C.
Give reason for the following:
Volumes of gases are converted into s.t.p. conditions and then compared.
The average energy per molecule is proportional to ______
Show that for monoatomic gas the ratio of the two specific heats is 5:3.
Show that for diatomic gas the ratio of the two specific heats is 7:5.
Estimate the average thermal energy of a helium atom at room temperature (27 °C).
A box of 1.00 m3 is filled with nitrogen at 1.50 atm at 300K. The box has a hole of an area 0.010 mm2. How much time is required for the pressure to reduce by 0.10 atm, if the pressure outside is 1 atm.
Cooking gas containers are kept in a lorry moving with uniform speed. The temperature of the gas molecules inside will ______.
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 ______.
Two tanks of equal volume contain equal mass of oxygen and nitrogen at 127°C. Find the ratio of pressure in two tanks.
