An aeroplane is flying at a height of 15 km, where the temperature is -50°C. Assuming $ k = 1.4 $ and $ R = 287 \, \text{J/K . kg} $, the approximate speed of the plane corresponding to $ M = 2.0 $ will be?

Question

Given $C_p = a + bT$
$a = 19.5$, $b = 0.042$, $n = 1$ mole
Temperature changes from $27^\circ C$ to $327^\circ C$.
Find $\Delta H$.

Answer 1

Step 1: Determine Mach number using its formula.
The Mach number, $ M $, is defined as: \[ M = \frac{v}{c} \] where $ v $ represents the plane's velocity and $ c $ signifies the speed of sound, calculated as: \[ c = \sqrt{k R T} \] In this context, $ T = -50^\circ \text{C} = 223.15 \, \text{K} $, $ k = 1.4 $, and $ R = 287 \, \text{J/K . kg} $. Therefore: \[ c = \sqrt{1.4 \times 287 \times 223.15} \approx 340.29 \, \text{m/s} \] Step 2: Compute the plane's velocity.
Given that $ M = 2.0 $, the velocity $ v $ is calculated as: \[ v = M \times c = 2.0 \times 340.29 \approx 680.58 \, \text{m/s} = 2055 \, \text{km/hour} \] Final Answer: \[ \boxed{2055 \, \text{km/hour}} \]

An aeroplane is flying at a height of 15 km, where the temperature is -50°C. Assuming \( k = 1.4 \) and \( R = 287 \, \text{J/K . kg} \), the approximate speed of the plane corresponding to \( M = 2.0 \) will be?

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The Correct Option is B

Solution and Explanation

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