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Physics-

General

Easy

Question

The p-V diagram of 2 g of helium gas for a certain process $A rightwards arrow B$ is shown in the figure. What is the heat given to the gas during the process $A rightwards arrow B ?$

$4 p_{0} V_{0}$
$6 p_{0} V_{0}$
$4.5 p_{0} V_{0}$
$2 p_{0} V_{0}$

The correct answer is: $6 p subscript 0 end subscript V subscript 0 end subscript$

Change in internal energy from A to B is
$increment U equals fraction numerator f over denominator 2 end fraction n R increment T equals fraction numerator f over denominator 2 end fraction left parenthesis p subscript f end subscript V subscript f end subscript minus p subscript i end subscript V subscript i end subscript right parenthesis$
$equals fraction numerator 3 over denominator 2 end fraction open parentheses 2 p subscript 0 end subscript cross times 2 V subscript 0 end subscript minus p subscript 0 end subscript cross times V subscript 0 end subscript close parentheses equals fraction numerator 9 over denominator 2 end fraction p subscript 0 end subscript V subscript 0 end subscript$
Work done in process A to B is equal to the area covered by the graph with volume axis, ie,
$W subscript A rightwards arrow B end subscript equals fraction numerator 1 over denominator 2 end fraction open parentheses p subscript 0 end subscript plus 2 p subscript 0 end subscript close parentheses cross times left parenthesis 2 V subscript 0 end subscript minus V subscript 0 end subscript right parenthesis equals fraction numerator 3 over denominator 2 end fraction p subscript 0 end subscript V subscript 0 end subscript$
Hence, $increment Q equals increment U plus increment W$
$equals fraction numerator 9 over denominator 2 end fraction p subscript 0 end subscript V subscript 0 end subscript plus fraction numerator 3 over denominator 2 end fraction p subscript 0 end subscript V subscript 0 end subscript equals 6 p subscript 0 end subscript V subscript 0 end subscript$

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