The dimensions of universal gas constant is

Options

A. `[M^(1)L^(1)T^(-2)K^(-1)mol^(-1)]`
B. `[M^(2)L^(2)T^(-2)K^(-1)mol^(-1)]`
C. `[M^(1)L^(2)T^(-2)K^(-1)mol^(-1)]`
D. `[M^(2)L^(1)T^(-2)K^(-1)mol^(-1)]`

Answer

C

Explanation

`PV=nRT`
`thereforeR=(PV)/(nT)" "thereforePV` has the dimensions of work
`thereforeR=W/(nT)=([M^(1)L^(2)T^(-2)])/([mol][K])`
`therefore[R]=[M^(1)L^(2)T^(-2)K^(-1)mol^(-1)]`