Question

The calorie is a unit of heat and it equals 4.2 J where 1 J = 1 kg m²/s².Suppose we employ a system of units in which unit of mass is α kg , unit of length is βm,unit of time γs.What will be the magnitude of calorie in the new system?

Answer 1

Explanation:

1 calorie = 4.2 j

1J = 1 kg m2s–2

put the value we get =>

1 calorie =4.2 kg m2s–2 = 4.2 × (1 kg) × (1 m2) × (1 s–2) …(1)

Given that

Unit of mass equals α kg => 1 kg mass = 1/α mass

Unit of length equals β m => 1 m length = 1/ β length

Unit of time is γs => 1 s time = 1/ γ time

Put the values in equation (1), we get

New unit of mass = α kg

=4.2 × (1 kg) × (1 m2) × (1 s–2)

= 4.2 × (1/ α ) × (1/ β ) 2 × (1/ γ) –2

= 4.2 × ( α–1 ) × (β–1 ) 2 × ( γ–1) –2

=4.2 α–1 β–2 γ2