A cylinder with a piston contains 0.338 mol of ideal gas at 5.10 x 10$ Pa and 349 K. Consider these paths: (1) The gas expands isobarically to 3.6 of its original volume. (2) It is then compressed isothermally back to its original volume. (3) It is cooled isochorically to its original pressure in the end.. a. Show the series of processes on a pV-diagram. b. Compute the temperature during the isothermal compression; c. Compute the maximum pressure; d. Compute the total work done by the piston on the gas during the series of processes. The Earth's atmosphere is composed of about 78 percent nitrogen, 21 percent oxygen, 0.9 percent argon, and 0.1 percent other gasses. To find out why these gasses are "trapped" in the earth's atmosphere, consider a projectile with mass m that is about to launch vertically upward from earth. a. Ignore air resistance, show that the projectile can only escape the magnetic pull of the earth if it is launched vertically upward with a kinetic energy greater than mgRearth, where g = 9.80 m/s? and the earth's radius Rearde = 6378 km. b. Compute the temperature required by a nitrogen molecule (molar mass 28.0 g/mol) and an oxygen molecule (molar mass 32 g/mol) to achieve the average translational kinetic energy required to escape earth? c. Repeat part (b) for the moon, for which g = 1.63 m/s? and Rmoon = 1740 km. d. Present your conclusion on the atmosphere of earth and moon based on the results from parts (b) and (c).

Related questions

Question

A cylinder with a piston contains 0.338 mol of ideal gas at 5.10 x 10$ Pa and 349
K. Consider these paths: (1) The gas expands isobarically to 3.6 of its original
volume. (2) It is then compressed isothermally back to its original volume. (3) It is
cooled isochorically to its original pressure in the end..
a. Show the series of processes on a pV-diagram.
b. Compute the temperature during the isothermal compression;
c. Compute the maximum pressure;
d. Compute the total work done by the piston on the gas during the series of
processes.

The Earth's atmosphere is composed of about 78 percent nitrogen, 21 percent
oxygen, 0.9 percent argon, and 0.1 percent other gasses. To find out why these
gasses are "trapped" in the earth's atmosphere, consider a projectile with mass m
that is about to launch vertically upward from earth.
a. Ignore air resistance, show that the projectile can only escape the magnetic
pull of the earth if it is launched vertically upward with a kinetic energy greater
than mgRearth, where g = 9.80 m/s? and the earth's radius Rearde = 6378 km.
b. Compute the temperature required by a nitrogen molecule (molar mass 28.0
g/mol) and an oxygen molecule (molar mass 32 g/mol) to achieve the average
translational kinetic energy required to escape earth?
c. Repeat part (b) for the moon, for which g = 1.63 m/s? and Rmoon = 1740 km.
d. Present your conclusion on the atmosphere of earth and moon based on the
results from parts (b) and (c).

Expert Solution

Step 1

Given,

The amount of ideal gas is $n = 0.338 (m o l)$

Initial pressure is $P_{i} = P_{o} = 5.1 \times 10^{5} (P a)$

Initial temperature is $T_{i} = T_{o} = 349 (K)$

So initial volume will be

$\begin{array}{rcl} V_{i} & = & V_{o} \\ = & \frac{n R T_{i}}{P_{i}} \\ = & \frac{0.338 (m o l) \times 8.314 (J . m o l^{- 1} . K^{- 1}) \times 349 (K)}{5.10 \times 10^{5} (P a)} \\ = & 1.92 \times 10^{- 3} (m^{3}) \end{array}$

According to the question,

1) gas first expand at constant pressure (isobaric expansion) to volume

2) Then it compressed at constant temperature (isothermal process) to its initial volume

3) Then it cooled down to its initial pressure at constant volume.

Step by step

Solved in 5 steps with 3 images

SEE SOLUTION Check out a sample Q&A here