What will be the ratio of stagnation temperature to critical temperature for isentropic flow of an ideal gas? [Consider ]

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  1. 1.0445
  2. 0.9721
  3. 0.8733
  4. 1.1445

Answer (Detailed Solution Below)

Option 4 : 1.1445
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Concept:

For isentropic flow of an ideal gas, the ratio of stagnation temperature T0 to critical temperature T* can be determined using the specific heat ratio γ. The critical temperature is the temperature at the throat (Mach number = 1) in a nozzle.

Given:

  • Specific heat ratio, \(γ = 1.289\)

Step 1: Recall the Stagnation-to-Critical Temperature Ratio Formula

The ratio is given by:

\[ \frac{T_0}{T^*} = \frac{γ + 1}{2} \]

This formula applies when the Mach number M is 1 (critical condition).

Step 2: Substitute the Given Value of γ

\[ \frac{T_0}{T^*} = \frac{1.289 + 1}{2} = \frac{2.289}{2} = 1.1445 \]

 

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