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Question

A gas is allowed to expand in a well insulated container against constant external pressure of 2.5atm from an initial volume of 2.50L to a final volume of 4.50L. The change in internal energy ΔU of the gas in joules will be ?


A

+505J

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B

+1136.25J

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C

-500J

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D

-505J

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Solution

The correct option is D

-505J


Explanation for the correct option:

Option(D):-505J

Step 1: Analyzing Given data:

The constant external pressure is given as= 2.5atm

The initial volume =2.50L

and final volume = 4.50L

Step 2: Formula for calculating ΔU:

According to the first law of thermodynamics, the formula related to the change in the internal energy can be given as:

ΔU=q+W

(whereΔU = change in internal energy of the system

q= heat transfer between the system

W=work done by the system)

Step 3: Calculation of ΔU:

Also, as per the given question, the gas is allowed to expand in a well-insulated container, hence, heat transfer i.e q=0

Hence,

ΔU=W=-PΔVΔU=W=-2.5atmx(4.50L2.50L)ΔU=W=-5.0LatmΔU=W=-5.0Latmx(101.33J/1Latm)ΔU=-505J

Hence, the change in internal energy ΔU of the gas in joules will be -505J.

Thus, option D is correct.


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