2.3 A calorie is a unit of heat (energy in transit) and it equals about 4.2 J where 1J = 1 kg m2 s–2. Suppose we employ a system of units in which the unit of mass equals α kg, the unit of length equals β m, the unit of time is γ s. Show that a calorie has a magnitude 4.2 α –1 β –2 γ 2 in terms of the new units.
2.3 A calorie is a unit of heat (energy in transit) and it equals about 4.2 J where 1J = 1 kg m2 s–2. Suppose we employ a system of units in which the unit of mass equals α kg, the unit of length equals β m, the unit of time is γ s. Show that a calorie has a magnitude 4.2 α –1 β –2 γ 2 in terms of the new units.
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1 Answer
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2.3
1 Calorie = 4.2 J = 4.2 kgm2s-2
Standard formula for conversion
Given unit / New unit = (M1/M2)x (L1/L2)y (T1/T2)z
Formula for energy = M1L2T-2
Here x = 1, y = 2, z = -2
In this problem
M1 = 1 kg, L1 = 1 m, T1 = 1 s and
M2 =? kg, L2 =? m, T2 =? s
So 1 Calorie = 4.2 (1/? )1 (1/? )2 (1/? )-2
= 4.2? -1? -2? 2
Similar Questions for you
According to question, we can write
Total moles of gas = n = nOxygen + nOxygen =
Volume of gas = 12 × 22.4 litre = 268.8 litre = 2.688 × 105 cm3
Viscosity = Pascal . Second
=
= x = 1, x + 2y = -1, -x + z = 1
y = -1, Z = 0
Viscosity = [P1A-1T0]
1 msD = 1mm
10 vsD = 9msD
1vsD = 0.9 MsD
L.C. = 1MSD – 1VSD = 1 – 0.9 = 0.1 mm
Zero error = 4LC = 0.4 mm
Reading = MSR + VSR + correction
= 4.1 cm + 6 * .01 cm + (-0.04 cm) = (4.1 + 0.06 – 0.04) cm
= 4.12 cm = 412 * 10-2 cm
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