An ideal monatomic gas is contained in a vessel of constant volume 0.400 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 18.0 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. 80.99 Correct: Your answer is correct. mol (I got this part correct)
(b) Find the specific heat of the gas.
(c) Find the change in temperature of the gas. Calculate the final temperature of the gas.
Apply the Ideal Gas Law to get, n , the number of moles :
n = ( P1 ) ( V1 ) / ( R ) ( T1 )
n = ( 5.00 atm ) ( 400 L ) / ( 0.08206 atm - L / mol - K ) ( 300 K )
n = 81.24 moles
Since the gas is monatomic :
Cpm = ( 5/2 ) ( R ) = ( 2.5 ) ( 8.314 J / mol - K ) = 20.785 J / mol - K
Cvm = ( 3/2 ) ( R ) = ( 1.5 ) ( 8.314 J /mol - K ) = 12.471 J / mol - K
No work is done by or on the gas since the volume is kept constant.
WB = 0.0 kJ
First Law of Thermodynamics gives :
Q = Delta U + WB
Delta U = Q - WB = ( 18.0 kJ ) - ( 0.0 kJ ) = 18.0 kJ
Delta U = ( n ) ( Cvm ) ( T2 - T1 )
T2 - T1 = ( Delta U ) / ( n ) ( Cvm )
T2 - T1 = ( 18000 J ) / ( 81.24 mol ) ( 12.471 J / mol - K )
T2 - T1 = 17.76 K
change in temperature = 17.6 K
T2 = T1 + ( T2 - T1 ) = 300 K + 17.6 K = 317.60 K
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