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Question
A calorie is a unit of heat or energy and it equals about 4.2 Jwhere 1J = 1 kg m2s–2. Suppose we employa system of units in which the unit of mass equals α kg, theunit of length equals β m, the unit of time is γs. Show that a calorie has a magnitude 4.2 α–1β–2 γ2in terms of the new units.
A calorie is a unit of heat or energy and it equals about 4.2 Jwhere 1J = 1 kg m2s–2. Suppose we employa system of units in which the unit of mass equals α kg, theunit of length equals β m, the unit of time is γs. Show that a calorie has a magnitude 4.2 α–1β–2 γ2in terms of the new units.
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Solution
Given that,
1 calorie = 4.2 (1 kg) (1 m2) (1 s–2)
New unit of mass = α kg
Hence, in terms of the new unit, 1 kg =
In terms of the new unit of length,
And, in terms of the new unit of time,
∴1 calorie = 4.2 (1 α–1) (1 β–2)(1 γ2) = 4.2 α–1β–2 γ2
Given that,
1 calorie = 4.2 (1 kg) (1 m2) (1 s–2)
New unit of mass = α kg
Hence, in terms of the new unit, 1 kg =
In terms of the new unit of length,
And, in terms of the new unit of time,
∴1 calorie = 4.2 (1 α–1) (1 β–2)(1 γ2) = 4.2 α–1β–2 γ2
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