Physics, asked by singhranjeet7374, 1 year ago

[P+a/(v square)] [v-b]=RT. :Here p is pressure a&b are constant. v is volume R is gas constant and T is temperature.Find the dimensions of [a] and[b].

Answers

Answered by sm9874252692
201
(P + a/V2) (V - b) = RT
P is pressure, V is volume and T is temperature.
[P] = [F/A] = [MLT −2/L2] = [ML−1T −2]
[V] = [L3]

We cannot add or subtract quantities of different dimensions. Therefore
[P] = [a/V2] ⇒ [a] = [PV2] = [ML−1T −2 L6] = [M L5 T −2]
∴ [a] = [M L5 T −2]

Similarly,
[b] = [V] = [L3]
Answered by CarliReifsteck
134

Answer:

The dimensions of a and b is [ML⁵T⁻²] and [L³].

Explanation:

Given that,

(P+\dfrac{a}{V^2})(V-b)=RT

Where, P = Pressure

V = Volume

T = Temperature

Pressure is the force upon area.

The dimension formula of pressure is

P = \dfrac{F}{A}

P =\dfrac{[MLT^{-2}]}{[L^2]}

P = [ML^{-1}T^{-2}]

The dimension formula of volume is

V =[L^{3}]

We cannot add or subtract quantities of different dimension.

Therefore,

P =\dfrac{a}{V^2}

a=PV^2

Put the dimension of P and V

a =[ML^{-1}T^{-2}][L^{6}]

a=[ML^{5}T^{-2}]

Similarly,

b=V

b = [L^{3}]

Hence, The dimensions of a and b is [ML⁵T⁻²] and [L³].

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