Question

One mole of an ideal gas expands adiabatically from an initial state(TA, V0) to a final state (Tf,5V0). Another mole of the same gas expands isothermally from a different initial state (TB, V0) to the same final state (Tf,5V0). The ratio of the specific heat of constant pressure and constant volume of the ideal gas is λ. What is the ratio of $\frac{T_A}{T_B}$?

• A. 5-γ
• B. 5γ-1
• C. 51+γ
• D. 51-γ

Answer 1

Answer: (B)

5γ-1

Answer 2

$T_AV_0^{\gamma-1}=T_B(5V_0)^{\gamma-1}$
$T_A=5^{\gamma-1}T_B$
$\frac{T_A}{T_B}=5^{\gamma-1}$

Firstly, there is an isothermal expansion from volume V to 33 V. Then, the volume is reduced from 33 V back to V while maintaining constant pressure.

(I) During the isothermal expansion, with T being constant: PV =nRT =constant This leads to the expression PV =constant, resulting in the characteristic hyperbolic curve.

(II) Subsequently, for the isobaric compression where P remains constant: PV =nRT