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 `DeltaT` of the substance. Using dimensional method, find the expression for s is ( Given that `[S]=[L^2 T^(-2)K^(-1)]`) is

Options

A. `QmDeltaT`
B. `Q/(mDeltaT)`
C. `"Qm"/(DeltaT)`
D. `m/(QDeltaT)`

Answer

To find the expression for the specific heat capacity \( s \) using dimensional analysis, we start with the relationship given by the formula for heat energy:

\[ Q = m \cdot s \cdot \Delta T \]

Where:
- \( Q \) is the heat energy,
- \( m \) is the mass,
- \( s \) is the specific heat capacity,
- \( \Delta T \) is the change in temperature.

### Step 1: Write down the dimensions of each quantity
We know the following dimensions:
- The dimension of heat energy \( Q \) is given as \( [Q] = [L^2 T^{-2}] \) (as energy has dimensions of work, which is force times distance).
- The dimension of mass \( m \) is \( [m] = [M] \).
- The dimension of change in temperature \( \Delta T \) is \( [\Delta T] = [K] \) (Kelvin).

### Step 2: Set up the dimensional equation
From the equation \( Q = m \cdot s \cdot \Delta T \), we can express the dimensions as:

\[ [L^2 T^{-2}] = [M] \cdot [s] \cdot [K] \]

### Step 3: Rearrange to find the dimension of specific heat capacity \( s \)
To isolate \( s \), we rearrange the equation:

\[ [s] = \frac{[L^2 T^{-2}]}{[M] \cdot [K]} \]

### Step 4: Substitute the dimensions into the equation
Now, substituting the dimensions we have:

\[ [s] = \frac{[L^2 T^{-2}]}{[M] \cdot [K]} = [L^2 M^{-1} T^{-2} K^{-1}] \]

### Conclusion
Thus, the expression for the specific heat capacity \( s \) in terms of its dimensions is:

\[ [s] = [L^2 M^{-1} T^{-2} K^{-1}] \]