\(50\%\) કાર્યક્ષમતા ધરાવતું એક કાર્નોટ એન્જિન \(600\,K\). તાપમાને રહેલ પ્રાપ્તિસ્થાન પાસેથી ઉષ્મા લે છે. ઠારણ વ્યવસ્થાનું તાપમાન બદલ્યા સિવાય તેની કાર્યક્ષમતા \(70 \%\) સુધી વધારવા માટે પ્રાપ્તિસ્થાનનું નવું તાપમાન \(................\,K\) હોવું જોઈખે.

A \(360\)
B \(1000\)
C \(900\)
D \(300\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(1000\)

Step-by-step Solution

Detailed explanation

\(\text { Initially } \eta=\frac{1}{2}\) \(\eta=1-\frac{ T _2}{ T _1}\) \(\therefore \frac{1}{2}=1-\frac{ T _2}{600} \quad \Rightarrow T _2=300\,K\) \(\Rightarrow \frac{ T _2}{600}=\frac{1}{2} \quad\) Now efficiency is increased to \(70 \%\) and \(T _2=300\) \(K\), Let temp of…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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