A gas expands adiabatically at constant pressure such that its temperature T propto (1/√V) . The value of (Cp/Cv) of gas is

Question

A gas expands adiabatically at constant pressure such that its temperature T propto (1/√V) . The value of (Cp/Cv) of gas is (A) 1.30 (B) 1.50 (C) 1.67 (D) 2.00

Tardigrade Admin · Accepted Answer

T propto (1/√V) TV(1/2)= constant For adiabatic process, TV&gamma; - 1= const. &gamma; -1=(1/2) ∴ &gamma; =(3/2)=1.50

Q. A gas expands adiabatically at constant pressure such that its temperature $T \propto \frac{1}{V}$ . The value of $\frac{C _{p}}{C _{v}}$ of gas is

$1.30$

$1.50$

$1.67$

$2.00$

$T \propto \frac{1}{V}$
$T V^{\frac{1}{2}} =$ constant
For adiabatic process, $T V^{γ - 1} =$ const.
$γ - 1 = \frac{1}{2}$
$∴ γ = \frac{3}{2} = 1.50$

Q. A gas expands adiabatically at constant pressure such that its temperature T∝V​1​ . The value of Cv​Cp​​ of gas is

1.30

1.50

1.67

2.00