Verified Solution • 2025–26 Session moderate

Q11.4: NCERT Physics - Part 2 THERMODYNAMICS 11.4 Solution: A cylinder with a movable piston contains 3 moles of hydrogen…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students frequently treat the insulated compression as isothermal and apply $P_1V_1=P_2V_2$, yielding a pressure factor of 2; the correct relation for an adiabatic process is $PV^{\gamma}=\text{const}$ with $\gamma=1.4$ for diatomic H$_2$, giving $P_2/P_1=(V_1/V_2)^{\gamma}=2^{1.4}$. Remember to use the appropriate $gamma$ for the gas and not the ideal‑gas isothermal law.

A cylinder with a movable piston contains 3 moles of hydrogen at standard temperature and pressure. The walls of the cylinder are made of a heat insulator, and the piston is insulated by having a pile of sand on it. By what factor does the pressure of the gas increase if the gas is compressed to half its original volume?

Step-by-Step Verified Solution

**Answer:** Pressure increases by a factor of 21.4=2.642^{1.4} = 2.64 **Step-by-Step Explanation:** The process is adiabatic (walls and piston insulated). For an adiabatic process:
PVγ=constantPV^\gamma = \text{constant}
For diatomic hydrogen, γ=1.4\gamma = 1.4.
P1V1γ=P2V2γP_1V_1^\gamma = P_2V_2^\gamma
P2P1=(V1V2)γ=(2)1.4=2.64\frac{P_2}{P_1} = \left(\frac{V_1}{V_2}\right)^\gamma = (2)^{1.4} = 2.64
Hence, the pressure increases by a factor of 2.64 .

All Questions in this Chapter

Q11.1 Q11.2 Q11.3 Q11.4 Q11.5 Q11.6 Q11.7 Q11.8

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