Question

efficiency of machines quick check
a rotating space heater used 1,400 joules of energy while heating a room. of that total, 896 joules
produced thermal energy, 181 joules produced kinetic energy, 203 joules produced light energy,
and 120 joules produced sound energy. what is the space heaters efficiency? (1 point)
56.25%
156.25%
64%
36%

Explanation:

Step1: Recall the efficiency formula

Efficiency ($\eta$) is given by the formula $\eta=\frac{\text{useful output energy}}{\text{total input energy}}\times100\%$. Here, the useful output energy is the thermal energy (since the purpose of a space - heater is to produce heat). The total input energy is the energy used by the heater.

Step2: Identify the values

The useful output energy (thermal energy) $E_{useful}=896$ joules and the total input energy $E_{total} = 1400$ joules.

Step3: Calculate the efficiency

Substitute the values into the formula: $\eta=\frac{896}{1400}\times100\%$.
First, calculate $\frac{896}{1400}=\frac{896\div56}{1400\div56}=\frac{16}{25}$ (using the property of equivalent fractions, dividing numerator and denominator by their greatest common divisor 56).
Then, $\frac{16}{25}\times100\%=(16\times4)\% = 64\%$.

Answer:

64%