Suppose that 5 moles of a monatomic ideal gas (atomic mass = 9.1 × 10^-27 kg) ar

Question

Suppose that 5 moles of a monatomic ideal gas (atomic mass = 9.1 × 10^-27 kg) are heated from 300 K to 500 K at a constant volume of 0.5 m^3. It may help you to recall that Cv = 12.47 J/K/mole and Cp = 20.79 J/K/mole for a monatomic ideal gas, and that the number of gas molecules is equal to Avagadro's number (6.022 × 10^23) times the number of moles of the gas.

1) How much energy (Joules) is transferred by heating during this process?

2) How much work (Joules) is done by the gas during this process?

3) What is the pressure of the gas (Pa) once the final temperature has been reached?

4) What is the average speed of a gas molecule (m/s) after the final temperature has been reached?

5)The same gas is now returned to its original temperature using a process that maintains a constant pressure. How much energy is transferred by heating during the constant-pressure process?

6)How much work was done on or by the gas during the constant-pressure process?

Explanation / Answer

1) Heat trnsferred,

Q = m Cv deltaT

and m = 5 x 6.022 x 10^23 x 9.1 x 10^-27

     = 0.0274 kg

Q = 0.0274 x 12.47 x (500 - 300) = 68.34 J .....Ans

2) for ischoric process, deltaV = 0

hence work done = 0

3) using PV = nRT

(P)(0.5) = (5)(8.314)(500)

P = 41570 pa

4) v = sqrt[ 3 R T / M ]

M = molar mass = 0.0274 kg / 5 =5.48 x 10^-3 kg

v = sqrt[ (3 x 8.314 x 500 / (5.48 x 10^-3) ]

   = 1508.55 m/s

5) Q = m Cp deltaT

= 0.0274 x 20.79 x - 200 = 113.93 J

6) V /T = constant

0.5 / 500 = Vf / 300

Vf = 0.3 m^3

W = P deltaV = (41570)(0.3 - 0.5) = -8314 J

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