Problem 77CP

FIGURE shows a thermodynamic process followed by 120 mg of helium.

a. Determine the pressure (in atm), temperature (in °C), and volume (in cm3 ) of the gas at points 1, 2, and 3. Put your results in a table for easy reading.

b. How much work is done on the gas during each of the three segments?

c. How much heat is transferred to or from the gas during each of the three segments?

FIGURE

Solution 77CP

Step 1 of 3

Part a

We are required to calculate the pressure, temperature and volume at the given points 1,2 and 3.

At the point 1, the pressure is 3 atm. The volume is 1000 cm3.

Pressure atm Pa

Volume cm3 = 0.001 m3

The mass of helium is mg = 120g

The molar mass of helium is 4.0 g.

Therefore, the number of moles of helium is = 30= 0.03 mole

Therefore, the temperature of helium at the point 1 is,

K

K

0C

0C

Therefore, at the point 1,

P1 |
V1 |
T1 |

3.0 atm |
1000 cm3 |
9420 C |

The system reaches point 2 after an isothermal expansion.

At this point, the volume is cm3 = 0.003 m3

The temperature is 9420 C as the process is isothermal.

The process is isothermal and the volume increases by three times. So, the pressure at this point will be reduced by three times. So, the pressure at the point 2 is 1 atm.

Therefore, at the point 2,

P2 |
V2 |
T2 |

1.0 atm |
3000 cm3 |
9420 C |

The system reaches point 3 at constant volume. This is followed by an adiabatic compression to state 1. Helium has .

Therefore, to calculate the pressure the point 3, we have to consider the following equation,

atm

atm

Therefore, the pressure at the point 3 is 0.48 atm.

For an adiabatic process, the temperature of the point 3 can be calculated from the following equation,

K

K

K

0C

0C

Therefore, the temperature at the point 3 is 3100C.

Therefore, at the point 3,

P3 |
V3 |
T3 |

0.48 atm |
3000 cm3 |
3100 C |