Question

Convert 1 watt-hour to Joule by dimensional analysis method.

Answer 1

Answer:

Joule is the unit for energy

Dimension Formula for Joule is [M¹L²T⁻²]

Let n1(joule)=n2(erg)

n1(M₁¹L₁²T₁⁻²]=n2[M₂¹L₂²T₂⁻²]

n2=n1(M₁¹L₁²T₁⁻²] /M₂¹L₂²T₂⁻²]

=n1x(M1/M2)¹x(L1/L2)²x(T1/T2)⁻²

=1x(1kg/gm)¹x(1m/1cm)²x(1s/1s)⁻²

=1x(1000g/gm)x(100cm/1cm)²x(1s/1s)⁻²

=10⁷

Therefore n1(joule)=n2(erg)

∴1 Joule=10⁷erg

Answer 2

Answer:

Joule is the unit for energy

Dimension Formula for Joule is [M¹L²T⁻²]

Let n1(joule)=n2(erg)

n1(M₁¹L₁²T₁⁻²]=n2[M₂¹L₂²T₂⁻²]

n2=n1(M₁¹L₁²T₁⁻²] /M₂¹L₂²T₂⁻²]

=n1x(M1/M2)¹x(L1/L2)²x(T1/T2)⁻²

=1x(1kg/gm)¹x(1m/1cm)²x(1s/1s)⁻²

=1x(1000g/gm)x(100cm/1cm)²x(1s/1s)⁻²

=10⁷

Therefore n1(joule)=n2(erg)

∴1 Joule=10⁷erg

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