Question

The dimensional formula of latent heat is:

• A. \( [M^0 L T^{-2}] \)
• B. \( [M L T^{-2}] \)
• C. \( [M^0 L^2 T^{-2}] \)
• D. \( [M L^2 T^{-2}] \)

Hint:

Latent heat is energy per unit mass, so its dimensional formula is derived by dividing energy (\( [M L^2 T^{-2}] \)) by mass (\( [M] \)), giving \( M^0 L^2 T^{-2} \).

Answer 1

The Correct Option is C

Step 1: {Define latent heat}
Latent heat (\( L \)) is defined as the amount of heat energy (\( Q \)) required to change the phase of a substance per unit mass: \[ L = \frac{Q}{m} \] Step 2: {Determine the dimensional formula of \( Q \)}
Heat energy (\( Q \)) is a form of energy, and its dimensional formula is the same as that of work: \[ [Q] = [M L^2 T^{-2}] \] Step 3: {Determine the dimensional formula of \( L \)}
Since mass (\( m \)) has the dimensional formula: \[ [m] = [M] \] we divide: \[ [L] = \frac{[Q]}{[m]} = \frac{[M L^2 T^{-2}]}{[M]} \] \[ = M^0 L^2 T^{-2} \] Step 4: {Verify the options}
Comparing with the given choices,
the correct answer is (C) \( M^0 L^2 T^{-2} \).

Answer 2

Given:
We are to find the dimensional formula of latent heat.

Step 1: Definition of latent heat
Latent heat (L) is defined as the amount of heat required to change the phase of a unit mass of a substance without any change in temperature.
\[ L = \frac{Q}{m} \] Where:
- \( Q \) = heat energy (dimensions of energy)
- \( m \) = mass

Step 2: Write dimensions
- Heat energy \( Q \) has dimensions of work or energy: \( [ML^2T^{-2}] \)
- Mass \( m \) has dimension: \( [M] \)

So,
\[ [L] = \frac{[ML^2T^{-2}]}{[M]} = [M^0 L^2 T^{-2}] \]

Final Answer:
The dimensional formula of latent heat is \( \boxed{[M^0 L^2 T^{-2}]} \)