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**Hint:**We have the temperature of sink as:${{T}_{1}}={{270}^{\circ }}C$ and temperature of source as: ${{T}_{2}}={{27}^{\circ }}C$. Also, heat supplied is: ${{Q}_{1}}=250\text{ }kJ{{s}^{-1}}$. So, by using the formula of efficiency of the heat engine, find the heat rejected: ${{Q}_{2}}$.

**Formula used:**

$\eta =1-\dfrac{{{T}_{1}}}{{{T}_{2}}}=1-\dfrac{{{Q}_{1}}}{{{Q}_{2}}}$, where $\eta $ is the efficiency of heat engine, ${{T}_{1}}$ is the initial temperature, ${{T}_{2}}$ is the final temperature, ${{Q}_{1}}$ is the heat supplied and ${{Q}_{2}}$ is the heat rejected.

**Complete step by step answer:**

We have:

$\begin{align}

& {{T}_{1}}={{227}^{\circ }}C \\

& {{T}_{2}}={{27}^{\circ }}C \\

& {{Q}_{1}}=250\text{ }kJ{{s}^{-1}} \\

\end{align}$

Now, convert all the temperatures from degree Celsius to degree Kelvin.

We have:

$\begin{align}

& {{T}_{1}}=227+273 \\

& =500K

\end{align}$

$\begin{align}

& {{T}_{2}}=27+273 \\

& =300K

\end{align}$

Now, by using the formula for efficiency of heat engine, we have:

$\begin{align}

& \eta =1-\dfrac{{{T}_{2}}}{{{T}_{1}}} \\

& =1-\dfrac{500}{300} \\

& =\dfrac{300-500}{300} \\

& =-\dfrac{200}{300} \\

& =-\dfrac{2}{3}......(1)

\end{align}$

Also, we know that, the efficiency of heat engine is equal to:

$\eta =1-\dfrac{{{Q}_{1}}}{{{Q}_{2}}}$

Now, by substituting the value of efficiency of the heat engine from equation (1), find the value of heat rejected.

We get:

$\begin{align}

& \Rightarrow -\dfrac{2}{3}=1-\dfrac{250}{{{Q}_{2}}} \\

& \Rightarrow \dfrac{250}{{{Q}_{2}}}=1+\dfrac{2}{3} \\

& \Rightarrow \dfrac{250}{{{Q}_{2}}}=\dfrac{5}{3} \\

& \Rightarrow {{Q}_{2}}=\dfrac{250\times 3}{5} \\

& \Rightarrow {{Q}_{2}}=150kJ{{s}^{-1}} \\

\end{align}$

So, the amount of heat rejected by the heat engine is $150kJ{{s}^{-1}}$ .

**So, the correct answer is “Option C”.**

**Additional Information:**

A heat engine is a device that converts heat to work. It takes heat from a reservoir then does some work like moving a piston, lifting weight etc and finally discharges some heat energy into the sink.

**Note:**

Remember to convert both the given temperatures in Kelvin scale first. The temperature can be converted by adding 273 to each given value of temperature.

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