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Concepts Of Physics MCQ Edition [Volume 2]PhysicsCalorimetry

Which of the following is true for the mechanical equivalent of heat?

Options

  1. AIt possesses the same dimensions as work.
  2. BIt possesses the same dimensions as heat.
  3. CIt possesses the same dimensions as energy.
  4. DIt is a dimensionless quantity.

Correct answer

D. It is a dimensionless quantity.

Step-by-step solution

According to the relation between work and heat, W = JH , where W is work, H is heat, and J is the mechanical equivalent of heat. Rearranging the formula, J = W H . Since both work and heat are forms of energy, their dimensional formulas are the same, which is [M L^2 T⁻²] . Substituting the dimensions, [J] = [M L^2 T⁻²] [M L^2 T⁻²] = [M^0 L^0 T^0] . Therefore, the mechanical equivalent of heat is a dimensionless quantity.

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