एक आदर्श गैस के n अणु कोई चक्रीय प्रक्रम ABCA (आरेख देखिए) करते है जिसमें नीचे दिए गए प्रक्रम होते हैं।

A → B : ताप T पर समतापीय प्रसार जिससे आयतन दो गुना, V1 से V2 = 2V1 और दाब P1 से P2 हो जाता है।

B → C : समदाबी संपीड़न-दाब P2  पर आरंभिक आयतन V1 तक होता है।

C → A : समआयतनिक परिवर्तन जिसमें दाब में परिवर्तन P1 से P2 होता है।

इस सम्पूर्ण चक्रीय प्रक्रम ABCA में किया गया कुल कार्य होगा :

  1. शून्‍य
  2. nRTln 2
  3. nRT
  4. nRT

Answer (Detailed Solution Below)

Option 4 : nRT
Free
JEE Main 04 April 2024 Shift 1
90 Qs. 300 Marks 180 Mins

Detailed Solution

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Explanation:

We know that,

Work Done in a p-v diagram = Area of Region ABCA

Area of Region ABCA = Area of region ABV2V- Area of region BV2V1

Since AB is an Isothermal process so work done in the process AB = Area of region ABV2V1 = nRTln() = nRTln(2) 

Area of region BV2V1= P2(V2 - V1) = P2V1

As process AB is Isothermal so TA= T= T=  =

∴ 2P2V1 = nRT

Hence, Work Done = nRTln(2) - P2VnRTln(2) -  = nRT (ln(2) - 

Hence, Option 4) is the correct choice.

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