Question

A motor cycle engine delivers a power of $10\text{kW}$ by consuming petrol at the rate of $2.4\text{kg/hr}$. Find the rate of heat rejection by the exhaust, if the calorific value of petrol is $35.5\text{MJ/kg}$.
(Neglect the other losses)

• A. $13.7\text{kW}$
• B. $23.7\text{kW}$
• C. $33.7\text{kW}$
• D. $13.7\text{W}$

Answer 1

The correct option is A $13.7\text{kW}$

Let $Q_1$ be the consumption of heat by engine, and $Q_2$ be the rejection of heat by engine, $W$ be the work done by engine
$\Rightarrow$The rate at which heat is consumed by engine will be,
$\frac{Q_1}{dt}=2.4\times 35.5\times {10}^6\text{J/hr}$
$\frac{Q_1}{dt}=\frac{85.2\times {10}^6}{3600}\text{J/sec}=23.7\text{kW}$
Rate of rejection of heat is given by $\frac{Q_2}{dt}$,
$\Rightarrow$Applying energy conservation,
$Q_1=Q_2+W...\left(i\right)$
$\Rightarrow Q_2=Q_1-W$
Differentiating both sides w.r.t time,
$\frac{d{Q}_2}{dt}=\frac{d{Q}_1}{dt}-\frac{dW}{dt}...\left(ii\right)$
where $\frac{dW}{dt}=10\text{kW}$, is the rate of workdone or the power delivered by engine.
$\Rightarrow \frac{d{Q}_2}{dt}=23.7\text{kW}-10\text{kW}$
$\therefore \frac{d{Q}_2}{dt}=13.7\text{kW}$
Hence, the rate of heat rejection by exhaust is $13.7\text{kW}$