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  • During an adiabatic process, the pressure of a gas is proportional to the cube of its absolute temperature. The value of <img alt="\mathrm{C_p / C_v}" src="https://entrancecorner.oncodecogs.co

During an adiabatic process, the pressure of a gas is proportional to the cube of its absolute temperature. The value of \mathrm{C_p / C_v} for that gas is:

Option: 1

\frac{3}{5}


Option: 2

\frac{4}{3}


Option: 3

\frac{5}{3}


Option: 4

\frac{3}{2}


Answers (1)

best_answer

For an adiabatic process

\mathrm{T P^n=k}

\mathrm{\text { Where } n=\frac{(1-\gamma)}{\gamma}, \gamma=\frac{C_p}{C_v} \text { and } k \text { is a constant }}

Therefore,

\mathrm{P=\left(\frac{k}{T}\right)^{1 / n}}

Since n = constant for a given gas,

\mathrm{P \propto T^{-1 / n}

\mathrm{\text { Given } P \propto T^3 \text { Hence }-\frac{1}{n}=3 \text { or }-\frac{\gamma}{1-\gamma}=3 \text {, Which }}

\mathrm{\text { Gives } \gamma=\frac{3}{2}}

Posted by

Rakesh

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