HC Verma: Concepts of Physics - Volume 2 Specific Heat Capacities of Gases Pages 77-80: Q18 Solution: Air ) is pumped at 2 atm pressure in a motor tyre at 20�C. If…

QPages 77-80: Q18: HC Verma: Concepts of Physics - Volume 2 Specific Heat Capacities of Gases Pages 77-80: Q18 Solution: Air ) is pumped at 2 atm pressure in a motor tyre at 20�C. If…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often use $P^{1-gamma}T^gamma= ext{const}$, which holds only for a reversible adiabatic process. A tyre burst is an irreversible expansion against the constant external pressure of the atmosphere, so the correct approach is to apply energy conservation: $Delta U = -P_{ ext{ext}}Delta V$ for an ideal gas, which shows that $T_2=T_1$ in this case. Avoid assuming isentropic behavior for sudden, non‑quasi‑static expansions.

Air

\gamma = 1.4

) is pumped at 2 atm pressure in a motor tyre at 20�C. If the tyre suddenly bursts, what would be the temperature of the air coming out of the tyre? Neglect any mixing with the atmospheric air.

Step-by-Step Verified Solution

**Answer:**

T_2 = 240.3

K. **Step-by-Step Explanation:** Given:

\gamma = 1.4

T_1 = 293

P_1 = 2

atm,

P_2 = 1

atm. Adiabatic relation:

P^{1-\gamma}T^\gamma = \text{constant}

P_1^{1-\gamma}T_1^\gamma = P_2^{1-\gamma}T_2^\gamma

2^{-0.4} \times 293^{1.4} = 1^{-0.4} \times T_2^{1.4}

T_2 = (2^{-0.4} \times 293^{1.4})^{1/1.4} = 240.3 \text{ K}

QPages 77-80: Q18: HC Verma: Concepts of Physics - Volume 2 Specific Heat Capacities of Gases Pages 77-80: Q18 Solution: Air ) is pumped at 2 atm pressure in a motor tyre at 20�C. If…

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