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Potential Energy of an Object at a Height

In an air sta...

Question

In an air standard diesel cycle the fuel cut off ratio is 2. If the temperature at the start of compression stroke is $27^{\circ} C,$ then the temperature (in K) at the end of expansion stroke is __________.
(Rounded upto one decimal place)
791.7

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Solution

The correct option is A 791.7
$\begin{matrix} \frac{T_{4}}{T_{1}} & = \frac{T_{4}}{T_{3}} \times \frac{T_{3}}{T_{2}} \times \frac{T_{2}}{T_{1}} = {(\frac{V_{3}}{V_{4}})}^{γ - 1} \times (\frac{V_{3}}{V_{2}}) \times {(\frac{V_{1}}{V_{2}})}^{- 1} = {(\frac{V_{3}}{V_{4}} \times \frac{V_{1}}{V_{2}})}^{γ - 1} \times (\frac{V_{3}}{V_{2}}) = {(\frac{V_{3}}{V_{2}})}^{γ - 1} \times \frac{V_{3}}{V_{2}} & [∵ V_{4} = V_{1}] = {(\frac{V_{3}}{V_{2}})}^{T} = 2^{1.4} = 2.64 \Rightarrow T_{4} & = T_{1} \times 2.64 = 300 \times 2.64 = 791.7 K \end{matrix}$

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