A calorie is a unit of heat or energy and it equals about 4.2 J where 1 J = 1 kgm2 s-2. Suppose we employ a system of units in which the unit of mass equals a kg, the unit of length equals j8 m, the. unit of time is ys. Show that a calorie has a magnitude 4.2 α-1 β-2 γ2 in terms of the new units.
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Answer:
It is said that the unit of mass, length and time is α kg, βm and γs. Let the new unit of calorie be P the old one is 4.2J = 4.2 [(kg)(m)2(s)−2]. Hence it is proved
Explanation:
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Explanation:
By standard formula of unit conversion,
Newunit
Givenunit
=(
M
2
M
1
)
2
(
L
2
L
1
)
2
(
T
2
T
1
)
2
Dimension formula of heat =[M
1
L
2
T
−2
]
∴ x=1,y=2,z=2
Since M
1
=1kg, L
1
=1m, T
1
=1s
and M
2
=α kg, L
2
=β m, T
2
=γ s
As 1 calorie =4.2 Joule
and 1 Joule =1kg m
2
s
−2
⇒
New unit
calorie
=4.2(
αkg
1kg
)
1
(
βm
1m
)
2
(
γs
1s
)
−2
∴ Calorie =4.2α
−1
β
−2
γ
2
New unit
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