4 . Suppose a tank contains 630 m³ of neon (Ne) at an absolute pressure of 1.50

Question

4. Suppose a tank contains 630 m³ of neon (Ne) at an absolute pressure of 1.50 × 105 Pa. The temperature is changed from 290 K to 318 K. What is the increase in the internal energy of the neon?
J

5. Suppose there are two identical gas cylinders. One contains the monatomic gas neon (Ne), and the other contains an equal mass of the monatomic gas radon (Rn). The pressures in the cylinders are the same, but the temperatures are different. Determine the ratio KENe/KERn of the average kinetic energy of an atom of neon to the average kinetic energy of an atom of radon.
  

Explanation / Answer

Problem 4)

The change in internal energy of a gas (or any fluid) is given by:

U = n*(u2 - u1)

If you assume the neon is calorically perfect, then this can be alternatively written as: U = n*cv*(T2 - T1)

where n is the number of moles of gas, cv is the molar isochoric specific heat of the gas, and T2 and T1 are the final and initial temperatures.

cv can be expressed in terms of the gas constant R (independant of gas flavor), and k, the adiabatic index, specific to the gas flavor. For all monatomic gasses (He, Ne, Ar, Kr, Xe), or even hydrogen when it exists monatomically on the sun, k=5/3.

cv = R/(k - 1)

Re-construct: U = n*R/(k - 1)*(T2 - T1)

Use the ideal gas law to find n*R

P1*V1 = n*R*T1

solve for n*R:
n*R = P1*V1/T1

Substitute:
U = P1*V1*(T2/T1 - 1)/(k - 1)

Data: P1:=150 kPa; V1:= 630 m^3; T1:= 290 K; T2:= 318 K; k:= 5/3;

do realize that 1 kPa * 1m^3 equals 1 kiloJoule.

Result: U = 13686.21 kiloJoules

According to Chegg guidelines I can answer one question at a time, so please post other questions separately. Please rate my answer...

Related Questions

Navigate

• Browse (All)
• Browse 4
• Subjects

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