Question

Which of the given dimensional formula represents heat capacity?

• A. \([ML^2 T^{-2} K^{-1}]\)
• B. \([ML^2 T^{-1} K^{-1}]\)
• C. \([ML^2 T^{-2} K^{-2}]\)
• D. \([MLT^{-2} K^{-1}]\)

Hint:

Remember that the dimensional formula for heat capacity is derived from the formula for energy (work) divided by the change in temperature. The unit of energy is Joules, which has the dimensional formula \([M L^2 T^{-2}]\), and temperature is measured in Kelvin.

Answer 1

The Correct Option is A

Heat capacity \(C\) is defined as the amount of heat required to change the temperature of a body by 1°C or 1K. The formula for heat capacity is: \[ C = \frac{Q}{\Delta T} \] Where: 
- \(Q\) is the heat added (in Joules), - \(\Delta T\) is the change in temperature (in Kelvin or Celsius). 
The dimensional formula for heat \(Q\) (in terms of work done or energy) is: \[ [Q] = [M L^2 T^{-2}] \] The dimensional formula for temperature \(\Delta T\) is: \[ [\Delta T] = [K] \] Thus, the dimensional formula for heat capacity \(C\) is: \[ [C] = \frac{[Q]}{[\Delta T]} = \frac{[M L^2 T^{-2}]}{[K]} = [M L^2 T^{-2} K^{-1}] \] Therefore, the correct dimensional formula for heat capacity is: \[ [M L^2 T^{-2} K^{-1}] \]