Statements (I): Dimensions of specific heat is, Statements (II): Dimensions of gas constant is

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Q.
Given below are two statements: [2024]

Statements (I): Dimensions of specific heat is $[L^{2} T^{- 2} K^{- 1}]$

Statements (Il): Dimensions of gas constant is $[M L^{2} T^{- 1} K^{- 1}]$

In the light of the above statements choose the most appropriate answer from the options given below:

1 Both statement (I) and statement (lI) are correct

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

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

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

Ans.
(3)

Specific heat, $s = \frac{∆ Q}{m ∆ T} = \frac{[M L^{2} T^{- 2}]}{[M K]} = [L^{2} T^{- 2} K^{- 1}]$

Statement-(I) is correct

$P V = n R T \Rightarrow R = \frac{P V}{n T}$

$[R] = \frac{[M L^{- 1} T^{- 2}] [L^{3}]}{[m o l] [K]}$

$[R] = [M L^{2} T^{- 2} m o l^{- 1} K^{- 1}]$

Statement-II is incorrect

Solution

Q.
Given below are two statements: [2024]

Statements (I): Dimensions of specific heat is $[L^{2} T^{- 2} K^{- 1}]$

Statements (Il): Dimensions of gas constant is $[M L^{2} T^{- 1} K^{- 1}]$

In the light of the above statements choose the most appropriate answer from the options given below:

1 Both statement (I) and statement (lI) are correct

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

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

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

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Solution

Q. Given below are two statements: [2024] Statements (I): Dimensions of specific heat is [L2T-2K-1] Statements (Il): Dimensions of gas constant is [ML2T-1K-1] In the light of the above statements choose the most appropriate answer from the options given below:

1 Both statement (I) and statement (lI) are correct

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

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

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

Ans. (3) Specific heat, s=∆Qm∆T=[ML2T-2][MK]=[L2T-2K-1] Statement-(I) is correct PV=nRT⇒R=PVnT [R]=[ML-1T-2][L3][mol][K] [R]=[ML2T-2mol-1K-1] Statement-II is incorrect

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Q.
Given below are two statements: [2024]

Statements (I): Dimensions of specific heat is $[L^{2} T^{- 2} K^{- 1}]$

Statements (Il): Dimensions of gas constant is $[M L^{2} T^{- 1} K^{- 1}]$

In the light of the above statements choose the most appropriate answer from the options given below: