Question

An ideal monatomic gas is contained in a vessel of constant volume 0.330 m3. The initial temperature and pressure of the gas are 300 K and 5.00 atm, respectively. The goal of this problem is to find the temperature and pressure of the gas after 24.0 kJ of thermal energy is supplied to the gas.

(a) Use the ideal gas law and initial conditions to calculate the number of moles of gas in the vessel. Your response differs from the correct answer by more than 10%. Double check your calculations. mol

(b) Find the specific heat of the gas. J/K

(c) What is the work done by the gas during this process? kJ

(d) Use the first law of thermodynamics to find the change in internal energy of the gas. kJ

(e) Find the change in temperature of the gas. K

(f) Calculate the final temperature of the gas. K (g) Use the ideal gas expression to find the final pressure of the gas. atm

Answer #1

part a:

volume=V=0.33 m^3

initial temperature=T1=300 K

initial pressure=P1=5 atm=5*101325 Pa=506625 Pa

then number of moles=P1*V/(R*T1)

where R=gas constant=8.314

then number of moles=506625*0.33/(8.314*300)=67

part b:

as it is a monoatomic has, specific heat at constant volume=(3/2)*R

=12.5 J.K^(-1) mol^(-1)

part c:

as volume remains constant, work done is 0.

part d:

from first law of thermodynamics:

energy supplied=change in internal eenrgy+work done by the system

here work done=0

then change in internal energy=heat supplied

=24 kJ

part e:

change in temperature=change in internal energy/(number of moles*specific heat)

=24000/(67*12.5)=28.657 degrees

part f:

final temperature=328.657 K

part g:

final pressure=initial pressure*final temperature/initial temperature

=5*328.657/300=5.4776 atm

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