Advertisements
Advertisements
Question
Estimate the total number of air molecules in a room of a capacity of 25 m3 at a temperature of 27°C.
Advertisements
Solution
T = 27°C + 273 = 300 K
kB = 1.38 × 10−23 J K−1
V = 25 m3
As Boltzmann’s Constant, kB = `"R"/"N"` ⇒ R = kBN
Now, PV = nRT = nkBNT
The number of molecules in the room,
nN = `"PV"/("k"_"B""T") = (1.013 xx 10^5 xx 25)/(1.38 xx 10^-23 xx 300)`
= `(25.325 xx 10^5)/(414 xx 10^-23)`
= 0.06117 × 1028
= 6.117 × 1026 molecules
nN = 6.1 × 1026 molecules
APPEARS IN
RELATED QUESTIONS
Find the kinetic energy of 3 litre of gas at S.T.P given standard pressure is 1.013 × 105 N/m2.
Two identically sized rooms A and B are connected by an open door. If the room A is air-conditioned such that its temperature is 4°C lesser than room B, which room has more air in it?
If the internal energy of an ideal gas U and volume V are doubled then the pressure ____________.
What is the microscopic origin of pressure?
According to the assumptions made in the kinetic theory of gases, when two molecules of a gas collide with each other, then ______.
Derive an expression for the pressure exerted by a gas on the basis of the kinetic theory of gases.
What is an ideal gas?
Does an ideal gas exist in practice?
Temperature remaining constant, if you double the number of molecules in a box, the pressure will ______.
The velocities of five molecules are 2 m/s, 3 m/s, 4 m/s, 5 m/s and 6 m/s. Find the root mean square velocity of molecules.
