Thermodynamics

JEE Main level, single correct, medium

102 of 190

Question 102 of 190

A hypothetical gas expands adiabatically such that its volume changes from 0808 litres to 2727 litres. If the ratio of final pressure of the gas to initial pressure of the gas is1681\dfrac{16}{81} . Then the ratio of CpCv\dfrac{{C}_{p}}{{C}_{v}} will be.

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Answer: (A) 43\dfrac{4}{3}

Let γ\gamma be the ratio of CpCv\dfrac{{C}_{p}}{{C}_{v}}.
Then for adiabatic process PVγ=P{V}^{\gamma }=Constant
⇒PiPf=(VfVi)γ\Rightarrow \dfrac{{P}_{i}}{{P}_{f}}={\left(\dfrac{{V}_{f}}{{V}_{i}}\right)}^{\gamma }
⇒(8116)=(278)γ⇒[(32)3]43=(278)γ\Rightarrow \left(\dfrac{81}{16}\right)={\left(\dfrac{27}{8}\right)}^{\gamma } \Rightarrow {\left[{\left(\dfrac{3}{2}\right)}^{3}\right]}^{\dfrac{4}{3}}={\left(\dfrac{27}{8}\right)}^{\gamma }
⇒γ=43\Rightarrow \gamma =\dfrac{4}{3}

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