Question

A calorie is a unit of heat or energy and it equals about 4.2 J where 1 J = 1 kgm^2 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.​

Answer 1

By standard formula of unit conversion,

$\frac{given \: unit}{new \: unit \: = ( \frac{m1}{m2} ) ^{2} ( \frac{l1}{l2}) {}^{2} ( \frac{t1}{t2} ) ^{2} }$

Dimension formula of heat= [M¹L²T-2]

..x = 1, y = 2, z = 2

Since M₁ = 1kg, L₁= 1m, T₁ = 1s

and M₂ = a kg, L2 = ßm, T2 = ys

As 1 calorie = 4.2 Joule

and 1 Joule = 1kg m²s-²

Calorie = 4.2a-¹B-²y² New unit

Answer 2

$\underline{\purple{\ddot{\MasterRohith}}}$

1 calorie = 4.2 (1kg)(1m^2)(1s^-2)

Here we should change all the units .

New unit of mass = a kg

• In terms of new unit 1kg
• 1kg=1/a
• 1lg=a^-1

Now , in terms of new length

• 1m= 1/Beta
• 1m= Beta^-1
• 1m^2=beta^-1

Now in terms new unit of time,

• 1s=1/teta
• 1s=teta^-1
• 1s^2=teta^-2
• 1s^-2=teta^2

Therefore, new unit

1calories = 4.2 alpha^-1beta^-2teta^-2.

Hope it helps u mate .

Thank you .