An equation is given here (P+(a/V2))=b (θ/V) where P= Pressure, V= Volume and θ= Absolute temperature. If a and b are constants, the dimensions of a will be

Question

An equation is given here (P+(a/V2))=b (θ/V) where P= Pressure, V= Volume and θ= Absolute temperature. If a and b are constants, the dimensions of a will be (A) [ML5T-2] (B) [M-1L5 T2] (C) [ML-5T-1] (D) [ML5 T1]

Tardigrade Admin · Accepted Answer

Equation (P+(a/V2))=b (θ/V). Since (a/V2) is added to the pressure, therefore dimensions of (a/V2) and pressure (P) will be the same. And dimensions of (a/V2)=(a/[ L 3]2)=[ ML -1 T -2] or a=[ ML 5 T -2].

Q. An equation is given here $(P + \frac{a}{V ^{2}}) = b \frac{θ}{V}$ where $P =$ Pressure, $V =$ Volume and $θ =$ Absolute temperature. If $a$ and $b$ are constants, the dimensions of $a$ will be

$[M L^{5} T^{- 2}]$

$[M^{- 1} L^{5} T^{2}]$

$[M L^{- 5} T^{- 1}]$

$[M L^{5} T^{1}]$

Equation $(P + \frac{a}{V ^{2}}) = b \frac{θ}{V}$ .
Since $\frac{a}{V ^{2}}$ is added to the pressure,
therefore dimensions of $\frac{a}{V ^{2}}$ and pressure $(P)$ will be the same.
And dimensions of $\frac{a}{V ^{2}} = \frac{a}{[ L ^{3} ] ^{2}} = [M L^{- 1} T^{- 2}]$
or $a = [M L^{5} T^{- 2}]$ .

Q. An equation is given here (P+V2a​)=bVθ​ where P= Pressure, V= Volume and θ= Absolute temperature. If a and b are constants, the dimensions of a will be

[ML5T−2]

[M−1L5T2]

[ML−5T−1]

[ML5T1]