One of the most efficient engines ever developed operates between $2100^{\circ} \mathrm{K}$ and $700

Question

One of the most efficient engines ever developed operates between $2100^{\circ} \mathrm{K}$ and $700^{\circ} \mathrm{K}$. Its actual efficiency is $40 \%$. This is $\mathrm{n} \%$ of its maximum possible efficiency where n is\

Professor PC Thomas Classes · Answer

Maximum possible efficiency $$ \begin{aligned} & =\left(\frac{\mathrm{T}_{1}-\mathrm{T}_{2}}{\mathrm{~T}_{1}}ight) 100=\left(\frac{2100-700}{2100}ight) 100 \ & =\frac{200}{3} \% \end{aligned} $$ Actual efficiency = 40\% $$ \begin{aligned} & \frac{	ext { Actualefficiency }}{	ext { Maximum possibleefficiency }} \ & =\frac{40}{\left(\frac{200}{3}ight)} 	imes 100 \% \ & \begin{array}{c} =\left(\frac{120}{200}ight) 	imes 100=\left(\frac{3}{5}ight) 	imes 100 \% \ =60 \% \end{array} \end{aligned} $$