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QPages 77-80: Q3: HC Verma: Concepts of Physics - Volume 2 Specific Heat Capacities of Gases Pages 77-80: Q3 Solution: The figure shows a cylindrical container containing oxygen )…

The figure shows a cylindrical container containing oxygen γ=1.4\gamma = 1.4) and closed by a 50-kg frictionless piston. The area of cross-section is 100 cm2100 \text{ cm}^2, atmospheric pressure is 100 kPa and g is 10 m s−210 \text{ m s}^{-2}. The cylinder is slowly heated for some time. Find the amount of heat supplied to the gas if the piston moves out through a distance of 20 cm.

Step-by-Step Verified Solution

**Answer:** Heat supplied = 1050 J. **Step-by-Step Explanation:** Given: γ=1.4\gamma = 1.4, piston mass = 50 kg, area = 100 cm_ = 10−210^{-2} m_, P0=100P_0 = 100 kPa, x=20x = 20 cm = 0.2 m. Work done:
W=(P0+mgA)Ax=(105+50×1010−2)×10−2×0.2=300 JW = \left(P_0 + \frac{mg}{A}\right) A x = \left(10^5 + \frac{50 \times 10}{10^{-2}}\right) \times 10^{-2} \times 0.2 = 300 \text{ J}
For adiabatic relation with constant pressure (isobaric process): Q=nCpΔT=γγ−1nRΔT=γγ−1WQ = nC_p\Delta T = \frac{\gamma}{\gamma-1} nR\Delta T = \frac{\gamma}{\gamma-1} W
Q=1.40.4×300=1050 JQ = \frac{1.4}{0.4} \times 300 = 1050 \text{ J}

All Questions in this Chapter

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