Question

Three moles of an ideal monatomic gas expands at a constant pressure of 3.5 atm; the volume of the gas changes from 3.0*10-2 m3 to 4.0*10-2 m3. (a) Calculate the initial and final temperatures of the gas. (a) Calculate the amount of work the gas does in expanding. (a) Calculate the change in internal energy of the gas.

Answer 1

Solution. (a) We use the equation

$$PV=\nu RT$$

where P=3.5 atm is pressure; V is volume; R=8.31 J/(mol K) is gas constant; T is temperature. Therefore initial temperature

$$T_1=\frac {PV} {\nu T}=\frac {3.5 \times 1.013 \times 10^5 \times 3 \times 10^{-2} } {3 \times 8.31}=427K$$

final temperature

$$T_2=\frac {PV} {\nu T}=\frac {3.5 \times 1.013 \times 10^5 \times 4 \times 10^{-2} } {3 \times 8.31}=569K$$

(b) For an isobaric process, work is equal to

$$W=p(V_2-V_1)=3.5 \times 1.013 \times 10^5 \times (4-3)\times 10^{-2}=3545.5J$$

(c) For ideal monatomic gas the change in internal energy is equal to

$$\Delta U= \frac {3} {2} \nu R \Delta T=1.3 \times 3 \times 8.31 \times (569-427)=5310.09J$$

Answer. (a) T1=427K; T2=569K; (b) 3545.5J; (c) 5310.09J