The entropy of any system is given by
${S}=\alpha^{2} \beta \ln \left[\frac{\mu {kR}}{J \beta^{2}}+3\right]$
Where $\alpha$ and $\beta$ are the constants. $\mu, J, K$ and $R$ are no. of moles, mechanical equivalent of heat, Boltzmann constant and gas constant repectively. [Take ${S}=\frac{{dQ}}{{T}}$ ]
Choose the incorrect option from the following:
The entropy of any system is given by
${S}=\alpha^{2} \beta \ln \left[\frac{\mu {kR}}{J \beta^{2}}+3\right]$
Where $\alpha$ and $\beta$ are the constants. $\mu, J, K$ and $R$ are no. of moles, mechanical equivalent of heat, Boltzmann constant and gas constant repectively. [Take ${S}=\frac{{dQ}}{{T}}$ ]
Choose the incorrect option from the following:
- [JEE MAIN 2021]
- A
${S}, \beta, {k}$ and $\mu {R}$ have the same dimensions.
- B
$\alpha$ and ${J}$ have the same dimensions.
- C
${S}$ and $\alpha$ have different dimensions.
- D
$\alpha$ and ${k}$ have the same dimensions.
Similar Questions
The dimensions of $\left(\frac{ B ^{2}}{\mu_{0}}\right)$ will be.
(if $\mu_{0}$ : permeability of free space and $B$ : magnetic field)
The dimensions of $\left(\frac{ B ^{2}}{\mu_{0}}\right)$ will be.
(if $\mu_{0}$ : permeability of free space and $B$ : magnetic field)
- [JEE MAIN 2022]
$A, B, C$ and $D$ are four different physical quantities having different dimensions. None of them is dimensionless. But we know that the equation $AD = C\, ln\, (BD)$ holds true. Then which of the combination is not a meaningful quantity ?
$A, B, C$ and $D$ are four different physical quantities having different dimensions. None of them is dimensionless. But we know that the equation $AD = C\, ln\, (BD)$ holds true. Then which of the combination is not a meaningful quantity ?
- [JEE MAIN 2016]
Match List $I$ with List $II$
LIST$-I$
LIST$-II$
$(A)$ Torque
$(I)$ $ML ^{-2} T ^{-2}$
$(B)$ Stress
$(II)$ $ML ^2 T ^{-2}$
$(C)$ Pressure of gradient
$(III)$ $ML ^{-1} T ^{-1}$
$(D)$ Coefficient of viscosity
$(IV)$ $ML ^{-1} T ^{-2}$
Choose the correct answer from the options given below
Match List $I$ with List $II$
| LIST$-I$ | LIST$-II$ |
| $(A)$ Torque | $(I)$ $ML ^{-2} T ^{-2}$ |
| $(B)$ Stress | $(II)$ $ML ^2 T ^{-2}$ |
| $(C)$ Pressure of gradient | $(III)$ $ML ^{-1} T ^{-1}$ |
| $(D)$ Coefficient of viscosity | $(IV)$ $ML ^{-1} T ^{-2}$ |
Choose the correct answer from the options given below
- [JEE MAIN 2023]
Consider two physical quantities A and B related to each other as $E=\frac{B-x^2}{A t}$ where $E, x$ and $t$ have dimensions of energy, length and time respectively. The dimension of $A B$ is
Consider two physical quantities A and B related to each other as $E=\frac{B-x^2}{A t}$ where $E, x$ and $t$ have dimensions of energy, length and time respectively. The dimension of $A B$ is
- [JEE MAIN 2024]
Dimensional formula for torque is
Dimensional formula for torque is
- [AIIMS 2002]