Question

1.
A gas is expanding according to the law pv"=C. Find C when p=80 v=3.1 and n=4/5



plz with full explanation not just the answer I need to solve my worksheet ​

Answer 1

The value of C is 197.788

Given that,

$PV^{n}=C$

Take log on both sides,

$logPV^{n}=logC\\(logAB= logA+logB)\\logP+logV^{n} =logC\\logC=logP+logV^{n}\\(logx^{n} =nlogx)\\logC=logP+nlogV\\logC=log80+\frac{4}{5} log3.1\\logC=1.9031+0.8*0.4914\\logC=1.9031+0.3931\\logC=2.2962$

Taking antilog on both sides

$antilog(logC)=antilog2.2962\\C=197.788$

Therefore the value of C is 197.788

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