COMEDK2024Morning ShiftPhysicsUnits and DimensionsActual
Which of the given dimensional formula represents heat capacity
Options
- 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 ]
Correct answer
A. [ ML ^2 ~T ⁻² ~K ⁻¹ ]
Step-by-step solution
Heat capacity C is defined as the amount of heat energy Q required to raise the temperature of a substance by an amount T . The formula is C = Q T . The dimensional formula for heat energy Q is the same as work or energy, which is [ML^2T⁻²] . The dimensional formula for temperature change T is [K] . Substituting these into the formula, we get C = [ML^2T⁻²] [K] = [ML^2T⁻²K⁻¹] . Answer: [ ML ^2 ~T ⁻² ~K ⁻¹ ]