## Q. 1.SP.2

Convert 200 Btu to (a) BG, (b) SI, and (c) cgs metric units of energy.

## Verified Solution

From inside the front cover:

$1 \mathrm{Btu}=778 \mathrm{ft} \cdot \mathrm{lb}, \quad 1 \mathrm{ft} \cdot \mathrm{lb}=1.356 \mathrm{~N} \cdot \mathrm{m}=1.356 \mathrm{~J}, \quad 1 \mathrm{~N}=10^{5}$ dyne.

(a) For BG units: $200 \mathrm{Btu}=200 \mathrm{Btu}\left(\frac{778 \mathrm{ft} \cdot 1 \mathrm{lb}}{1 \mathrm{Btu}}\right)=155,600 \mathrm{ft} \cdot \mathrm{lb}$.

(b) For SI units: $155,600 \mathrm{ft} \cdot \mathrm{lb}=155,600 \mathrm{ft} \cdot \mathrm{lb}\left(\frac{1.356 \mathrm{~N} \cdot \mathrm{m}}{1 \mathrm{ft} \cdot \mathrm{lb}}\right)$

$=210994 \mathrm{~N} \cdot \mathrm{m}=211 \mathrm{kN} \cdot \mathrm{m}=211 \mathrm{~kJ}$.

(c) For cgs units: $210994 \mathrm{~N} \cdot \mathrm{m}=211 \times 10^{3} \mathrm{~N} \cdot \mathrm{m}\left(\frac{10^{5} \mathrm{dyne}}{1 \mathrm{~N}}\right)\left(\frac{10^{2} \mathrm{~cm}}{\mathrm{~m}}\right)$

$=211 \times 10^{10}$ dyne $\cdot \mathrm{cm}=211 \times 10^{10} \mathrm{erg}$.