Question 21: Units , Dimensions and Error Analysis

Question

Which of the given dimensional formula represents heat capacity

Accepted Answer

To determine which dimensional formula represents heat capacity, we need to analyze the quantities involved in the definition of heat capacity. Heat capacity, symbolized as $C$, is the amount of heat energy required to raise the temperature of a substance by one unit of temperature. Mathematically, it can be expressed as:
$$ C = \frac{Q}{\Delta T} $$
where $Q$ is the heat added (energy) and $\Delta T$ is the change in temperature.
Next, we need to express the dimensional formulas of the quantities involved:
1. Heat energy $Q$ has the dimensional formula of energy, which is:
$$ [Q] = [\mathrm{ML}^2 \mathrm{T}^{-2}] $$
2. Temperature $\Delta T$ has the dimensional formula of:
$$ [\Delta T] = [\mathrm{K}] $$
Using these, we find the dimensional formula for heat capacity $C$:
$$ [C] = \frac{[Q]}{[\Delta T]} = \frac{[\mathrm{ML}^2 \mathrm{~T}^{-2}]}{[\mathrm{K}]} = [\mathrm{ML}^2 \mathrm{T}^{-2} \mathrm{~K}^{-1}] $$
Therefore, the dimensional formula for heat capacity is:
$$ [\mathrm{ML}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}] $$
Comparing this with the options given, the correct answer is Option A:
$$ \left[\mathrm{ML}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}\right] $$

Answer

$$\left[\mathrm{ML}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}\right]$$

Answer

$$\left[\mathrm{ML}^2 \mathrm{~T}^{-1} \mathrm{~K}^{-1}\right]$$

Answer

$$\left[\mathrm{ML}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-2}\right]$$

Answer

$$\left[\mathrm{MLT}^{-2} \mathrm{~K}^{-1}\right]$$

Units , Dimensions and Error Analysis

Which of the given dimensional formula represents heat capacity

Choose the correct answer: