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(B) The heat energy $Q$ is given by the relation $Q = m^a s^b (\Delta T)^c$.The dimensions of the quantities are:$[Q] = [M L^2 T^{-2}]$$[m] = [M]$$[s]

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$\frac{Q}{m \Delta T}$

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(B) The heat energy $Q$ is given by the relation $Q = m^a s^b (\Delta T)^c$.The dimensions of the quantities are:$[Q] = [M L^2 T^{-2}]$$[m] = [M]$$[s] = [L^2 T^{-2} K^{-1}]$$[\Delta T] = [K]$Substituting these into the equation:$[M L^2 T^{-2}] = [M]^a [L^2 T^{-2} K^{-1}]^b [K]^c$$[M L^2 T^{-2}] = [M^a L^{2b} T^{-2b} K^{-b+c}]$Comparing the powers of $M, L, T,$ and $K$ on both sides:For $M$: $a = 1$For $L$: $2b = 2 \Rightarrow b = 1$For $T$: $-2b = -2 \Rightarrow b = 1$For $K$: $-b + c = 0 \Rightarrow c = b = 1$Thus,the expression is $Q = m^1 s^1 (\Delta T)^1$,which simplifies to $Q = m s \Delta T$.Rearranging for $s$,we get $s = \frac{Q}{m \Delta T}$.

The amount of heat energy $Q$ used to heat up a substance depends on its mass $m$,its specific heat capacity $s$,and the change in temperature $\Delta T$ of the substance. Using the dimensional method,find the expression for $s$. (Given that $[s] = [L^2 T^{-2} K^{-1}]$)

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