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 force $F$ is given in terms of time $t$ and displacement $x$ by the equation $F = A\,cos\,Bx + C\,sin\,Dt.$ The dimensional formulae of $D/B$ is
The force $F$ is given in terms of time $t$ and displacement $x$ by the equation $F = A\,cos\,Bx + C\,sin\,Dt.$ The dimensional formulae of $D/B$ is
$Assertion$ : Specific gravity of a fluid is a dimensionless quantity.
$Reason$ : It is the ratio of density of fluid to the density of water
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$Reason$ : It is the ratio of density of fluid to the density of water
- [AIIMS 2005]
If force $(F),$ velocity $(V)$ and time $(T)$ are taken as fundamental units, then the dimensions of mass are
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- [AIPMT 2014]
A calorie is a unit of heat or energy and it equals about $4.2\; J$ where $1 \;J =1\; kg \,m ^{2} \,s ^{-2}$ Suppose we employ a system of units in which the unit of mass equals $\alpha\; kg$, the unit of length equals $\beta\; m$, the unit of time is $\gamma$ $s$. Show that a calorie has a magnitude $4.2 \;\alpha^{-1} \beta^{-2} \gamma^{2}$ in terms of the new units.
Match List$-I$ with List$-II.$
List$-I$
List$-II$
$(a)$ Torque
$(i)$ ${MLT}^{-1}$
$(b)$ Impulse
$(ii)$ ${MT}^{-2}$
$(c)$ Tension
$(iii)$ ${ML}^{2} {T}^{-2}$
$(d)$ Surface Tension
$(iv)$ ${ML} {T}^{-2}$
Choose the most appropriate answer from the option given below :
| List$-I$ | List$-II$ |
| $(a)$ Torque | $(i)$ ${MLT}^{-1}$ |
| $(b)$ Impulse | $(ii)$ ${MT}^{-2}$ |
| $(c)$ Tension | $(iii)$ ${ML}^{2} {T}^{-2}$ |
| $(d)$ Surface Tension | $(iv)$ ${ML} {T}^{-2}$ |
- [JEE MAIN 2021]