A calorie is a unit of heat or energy and it equals about 4.2j where 1j= 1kgm suppose we employ a system of units in which the unit of mass equals a kg.the unit of length equals b m.,the unit of time is y s. show that a calorie has a magnitude 4.2a^-3 b^-2y^3 in terms of the new unit.
Answers
Solution
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
Answer:
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