Vi 3. A sample of n moles of an ideal gas, originally at pressure P, and volume

Question

Vi 3. A sample of n moles of an ideal gas, originally at pressure P, and volume V, undergoes the three processes shown on the PV diagram above: The volume is halved while the pressure remains constant. The pressure is increased while the volume remains constant until the temperature reaches its original value. The volume is increased while the temperature remains constant until the volume reaches its original value Process 1 2: Process 2 3: Process 3 1: Determine expressions for each of the following in terms of P, Vi, n, and fundamental constants. a. i. The temperature of the gas in state i. The temperature of the gas in state 1 ii. The pressure of the gas in state 3 iii. The total work done on the gas during processes 1 2 and 2 3

Explanation / Answer

a) i. P1*V1 = nRT1
T1 = P1*V1/nR
ii. from 1 to 2, pressure is constant
Work done on the gas = P*V1/2
and P1V1/2 = nRT2
T2 = P1V1/nR

But, T3 = T1
so, P3*V1/2 = n*R*T1
P3 = n*R*T1*2/V1
iii. Total work doneon the gas = P1V1/2 - nRT*ln(2)

b. From 2 to 3, Work done is 0, but P rises, so does T, so heat is added to the system
c. From 3 to 1, T is constant, and gas expands, so heat is added to the gas (which enables it to work)

Related Questions

Navigate

• Browse (All)
• Browse V
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.