Question

The equation of a gas is given by : $PV=AT+B{T}^2$, where $P=$ pressure, $V=$ volume, $T=$ temperature. The dimensions of constant B are

• A. $\left[M{L}^2{T}^{-4}\right]$
• B. $\left[M{L}^2{T}^{-2}{\theta }^{-2}\right]$
• C. $\left[ML\right]$
• D. $\left[M{L}^2{T}^{-2}\right]$

Answer 1

The correct option is B $\left[M{L}^2{T}^{-2}{\theta }^{-2}\right]$

We know the dimension of P and V, using that dimension of PV

$\left[PV\right]=\left[M{L}^2{T}^{-2}\right]$,

The dimension of PV will be equal to the remaining two, which are being added. Equating the dimension
$\left[AT\right]=\left[M{L}^2{T}^{-2}\right]$
$\left[B{T}^2\right]=\left[M{L}^2{T}^{-2}\right]$
$\left[B\right]=\left[M{L}^2{T}^{-2}{\theta }^{-2}\right]$