Physics, asked by saritarai57360, 9 months ago

from dimensional analysis derive the unit of 'M' in the equation Pv =WRT/M where the symbols have their usual meaning ​

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Answered by abhi178
14

The unit of M in given equation is g/mol.

From dimensional analysis, we have to derive the unit of M in the equation, PV = WRT/M, where the symbols have their usual meaning.

solution : method 1 : We know from gaseous equation, PV = nRT

but here PV = WRT/M

so, WRT/M = nRT

⇒W/M = n

⇒M = W/n

here W is weight and n is no of moles.

so, unit of W = g and unit of n = mol

then unit of M = g/mol

Therefore the unit of M in equation PV = WRT/M, is g/mol

method 2 : in equation, PV = WRT/M

P = pressure ⇒dimensions of P = [ML¯¹T¯²]

V = volume ⇒ dimensions of V = [L³]

W = weight in g ⇒dimensions of W = [M]

R = universal gas constant ⇒dimensions of R = [ML²T¯²θ¯¹mol¯¹],

T = temperature ⇒dimensions of T = [θ]

now,

[ML¯¹T¯²][L³] = [M][ML²T¯²θ¯¹mol¯¹][θ]/M

⇒[ML²T¯²] = [M²L²T¯²mol¯¹]/M

⇒M = [M mol¯¹]

Therefore the unit of M = unit of Mass/unit of mole = g/mol.

Answered by sujal6127
0

Answer:

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