Question

Please help me to convert 1kWh into J using dimensional analysis.

Answer 1

1 watt is defined as 1 joule/second. So if you multiply a watt times seconds, you get Ws which is also a joule.

So 1kW is 1000W, and an hour is 60 seconds x 60 minutes.

So 1kWh = 3600kWs = 3,600,000Ws = 3,600,000J

this is the right method ,
bcz KWh and Joule are SI system. Dimensional method is used for conversion of one system to another i.e CGS , MKS, SI system etc....it is because there only change in unit is there i.e unit of mass in cgs is gram , in MKS is pounds ,in SI is kilograms.


KWhr and Joule is the unit of energy

Dimension Formula for energy is [M^1 L^2 T^-2]

Let na(KWhr)=nb(Joule)

na(Ma^1 La^2 Ta^-2)
= nb (Mb^1 Lb^2 Tb^-2)

nb = na [(Ma÷Mb)^1 (La÷Lb)^2 (Ta÷Tb)^-2]

here we want 1 Kwh=1000 Wh
=3600× 1000 J/second ×second
=3600000
so na =3600000
also apply unit based for each terms,
other units of these two term are same except time.

nb=3600000 × [(1kg ÷1kg)^1 ×(1m ÷1m)^2 × (1 second÷1second)^-2]

=3600000× 1×1×1
=3600000.

so 1 KWh=3600000 J/s.

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