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Physics-

General

Easy

Question

An ideal gas is taken from point A to the point B, as shown in the p-V diagram, keeping the temperature constant. The work done in the process is

$(p_{A} - p_{B}) (V_{B} - V_{A})$
$\frac{1}{2} (p_{B} - p_{A}) (V_{B} + V_{A})$
$\frac{1}{2} (p_{B} - p_{A}) (V_{B} - V_{A})$
$\frac{1}{2} (p_{A} + p_{B}) (V_{B} - V_{A})$

The correct answer is: $fraction numerator 1 over denominator 2 end fraction open parentheses p subscript A end subscript plus p subscript B end subscript close parentheses left parenthesis V subscript B end subscript minus V subscript A end subscript right parenthesis$

The p-V diagram is shown below

Work done =area of ABCDEA
$equals a r e a blank o f increment A B E plus a r e a blank o f blank r e c t a n g l e B C D E$
$equals fraction numerator 1 over denominator 2 end fraction open parentheses p subscript A end subscript minus p subscript B end subscript close parentheses open parentheses V subscript B end subscript minus V subscript A end subscript close parentheses plus p subscript B end subscript left parenthesis V subscript B end subscript minus V subscript A end subscript right parenthesis$
$equals open square brackets fraction numerator 1 over denominator 2 end fraction open parentheses p subscript A end subscript minus p subscript B end subscript close parentheses plus p subscript B end subscript close square brackets left parenthesis V subscript B end subscript minus V subscript A end subscript right parenthesis$
$equals fraction numerator 1 over denominator 2 end fraction open parentheses p subscript A end subscript plus p subscript B end subscript close parentheses left parenthesis V subscript B end subscript minus V subscript A end subscript right parenthesis$

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