Given below are two statements: Statement (I): dimensions of specific heat is [L2 T-2 K-1 ] Statement (II): dimensions of gas constant is [ML2 T-1 K-1 ]

(A) Statement (I) is incorrect but statement (II) is correct

(B) Both statement (I) and statement (II) are incorrect

(D) Both statement (I) and statement (II) are correct

JEE Mains · Physics · STD 11 - Units,dimensions and measurement

Given below are two statements : Statement \((I)\) : dimensions of specific heat is \(\left[\mathrm{L}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}\right]\) Statement \((II)\) : dimensions of gas constant is \(\left[\mathrm{ML}^2 \mathrm{~T}^{-1} \mathrm{~K}^{-1}\right]\)

Pick an option to check your answer.

Verified Solution

Correct Answer

(C) Statement \((I)\) is correct but statement \((II)\) is incorrect

Detailed explanation

\(\Delta \mathrm{Q}=\mathrm{mS} \Delta \mathrm{T}\)

\(\mathrm{s}=\frac{\Delta \mathrm{Q}}{\mathrm{m} \Delta \mathrm{T}}\)

\({[\mathrm{s}]=\left[\frac{\mathrm{ML}^2 \mathrm{~T}^{-2}}{\mathrm{MK}}\right]}\)

\({[\mathrm{s}]=\left[\mathrm{L}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}\right]}\)

Statement-\((I)\) is correct

\(\mathrm{PV}=\mathrm{nRT} \Rightarrow \mathrm{R}=\frac{\mathrm{PV}}{\mathrm{nT}}\)

\({[\mathrm{R}]=\frac{\left[\mathrm{ML}^{-1} \mathrm{~T}^{-2}\right]\left[\mathrm{L}^3\right]}{[\mathrm{mol}][\mathrm{K}]}}\)

\({[\mathrm{R}]=\left[\mathrm{ML}^{-2} \mathrm{~T}^{-2} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}\right]}\)

Statement\(-II\) is incorrect

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