Question

In this problem, 0.90 mole of a monatomic ideal gas is initially at 285 K and 1 atm.

(a) What is its initial internal energy?

_____ kJ

(b) Find its final internal energy and the work done by the gas when 420 J of heat are added at constant pressure.

final internal energy ________kJ

work done by the gas _______kJ

(c) Find the same quantities when 420 J of heat are added at constant volume.

finale internal energy ________kJ

work done by the gas ________kJ

Answer #1

f is degree of freedom, n is number of moles and T is tempreture of
gas in Kelvin, R=8.3, is gas constant

f = 3 for monoatomic gas

a) So U_{i} = 3x0.9x8.3x285/2= 3.2 KJ

b) Heat given to gas at constant pressure is

Q = n C_{p} ( dleta T) C_{p} is molar specific heat
at constant pressure and = (f+2)R/2 , (delta T) is chsnge in
tempreture during process

hence 420 = 0.9 x 5 x 8.3x (delta T)/2

Hence (delta T) = 22.5 K

Work done by gas at constant pressure is

W = n R (delta T) = 0.9x 8.3 x22.5 = 0.17 KJ

Q = (delta U) + W

hence (delta U) = 0.42 - 0.17 = 0.25 KJ

So U_{f} = 3.2 + 0.25 = 3.45 KJ

c) Work done by gas during constant volume process = 0

Hence at constant volume (delta U) = Q = 0.42 KJ

and U_{f} = 3.62 KJ

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