A portion of a cylinder is filled with one mole of monatomic ideal gas at P = 1 atm and T = 300 K. A massless piston of area A attached to a spring in equilibrium (under vacuum) separates the gas from the other section of the cylinder (as in the figure below). The cylinder is thermally insulated from the rest of world, and the piston is fixed to the cylinder initially and then released. After reaching equilibrium, the volume occupied by the gas is double the original. Neglecting the heat capacities of the cylinder, piston and spring, find the temperature and pressure of the gas.
Added by Joan C.
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First, we know that the initial pressure, volume, and temperature of the gas are given as P1 = 1 atm, V1, and T1 = 300 K. Show more…
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The drawing shows an ideal gas confined to a cylinder by a massless piston that is attached to an ideal spring. Outside the cylinder is a vacuum. The cross-sectional area of the piston is $A=2.50 \times 10^{-3} \mathrm{m}^{2}$ The initial pressure, volume, and temperature of the gas are, respectively, $P_{0}, V_{0}=6.00 \times 10^{-4} \mathrm{m}^{3},$ and $T_{0}=273 \mathrm{K},$ and the spring is initially stretched by an amount $x_{0}=0.0800 \mathrm{m}$ with respect to its unstrained length. The gas is heated, so that its final pressure, volume, and temperature are $P_{\mathrm{f}}, V_{\mathrm{f}},$ and $T_{\mathrm{f}},$ and the spring is stretched by an amount $x_{\mathrm{f}}=0.1000 \mathrm{m}$ with respect to its unstrained length. What is the final temperature of the gas?
The drawing shows an ideal gas confined to a cylinder by a massless piston that is attached to an ideal spring. Outside the cylinder is a vacuum. The cross-sectional area of the piston is A = 2.50 × 10-3 m2. The initial pressure, volume, and temperature of the gas are, respectively, P0, V0 = 6.00 × 10-4 m3 and T0 = 273 K, and the spring is initially stretched by an amount x0 = 0.091 m with respect to its unstrained length. The gas is heated, so that its final pressure, volume, and temperature are Pf, Vf and Tf and the spring is stretched by an amount xf = 0.11 m with respect to its unstrained length. What is the final temperature of the gas?
Hubert A.
In the arrangement shown in Fig. $12.17$, gas is thermally insulated. An ideal gas is filled in the cylinder having pressure $P$ greater than atmospheric pressure $P_{0}$. The spring of force constant $K$ is initially upstretched. The piston of mass $m$ and area s is frictionless. In equilibrium, the piston rises up a distance $x_{0}$, then (A) Final pressure of the gas is $P_{0}+\frac{K x_{0}}{s}+\frac{m g}{s}$. (B) Work done by the gas is $\frac{1}{2} K x_{0}^{2}+m g x_{0}$. (C) Decrease in internal energy of the gas is $\frac{1}{2} K x_{0}^{2}+m g x_{0}+P_{0} s x_{0}$ (D) All of the above.
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