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Question

Two litre of N2 at 0oC and 5 atm are expanded isothermally against a constant external pressure of 1 atm until the pressure of gas reaches 1 atm. Assuming the gas to be ideal calculate work of expansion?

A
504.2joule
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B
405.2joule
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C
+810.4joule
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D
810.4joule
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Solution

The correct option is A 504.2joule
Given:-P1=5 atm
P2=1 atm
V2=2 litres

Solution:-
Initially the gas is at 5 atm pressure and it's volume is 2 liter. The final pressure is going to be decreased to 1 atm. Process is isothermal means the temperature is constant. Using Boyle's law we calculate the final volume of the gas:

P1V1=P2V2

Let's plug in the values in the equation to calculate final volume:

5 atm×(2L)=1 atm.(V2)

V2=10 liters

External pressure is also given as 1 atm. Pressure-volume work is calculated using the formula:

w=PextΔV

w=1atm(10L5L)

w=5 atmL

since, 1 atmL=101.325J

So, 5 atmL(101.325J1 atmL)

=504.2 J

Hence the correct option is A

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