Question

In a motor, the electrical power input is $500W$ and the mechanical power output is $0.54$ horse power. The heat developed in the motor in $1$ hour is (assuming that all the electric energy which is not converted to mechanical energy is converted to heat) is

• A. $4.18\times 10^{4}cal$
• B. $3.6\times 10^{5}cal$
• C. $8.6\times 10^{4}cal$
• D. $1.28\times 10^{5}cal$

Answer 1

Answer: (C)

$\text{Efficiency}=\frac{\text{0.54}\times 746}{500}=\text{0.80}$ or $80\%$
( $0.5kW=500W$ and $0.54hp=0.54\times 746W$ )
$\therefore$ 80% of the electrical energy is converted to mechanical energy and the rest 20% is converted to heat energy.
$\therefore \frac{20}{100}\times 500=100W$ of power is converted to heat
$\therefore$ Heat produced in 1h (or 3600 s)
$=100\times 3600=36\times 10^{4}J$
$=\frac{36\times 10^4}{\text{4.18}}\text{cal}=\text{8.6}\times 10^{4}cal$