Question

Under constant pressure, the temperature of 1.70 mol of an ideal monatomic gas is raised 15.5 K. (a) What is the work W done by the gas? J (b) What is the energy transferred as heat Q? J (c) What is the change ΔEint in the internal energy of the gas? J (d) What is the change ΔK in the average kinetic energy per atom? J

Answer #1

a)At constant pressure, work done by gas

W = nR ΔT

n is number of moles of gas, R (gas constant) = 8.3

so W = 1.7 x 8.3 x 15.5 = 218.7 J

b) At constant pressure Q = n C_{p} ΔT

C_{p} is molar specific heat at constant pressure and =
(f+2)R/f

f is degree of freedom. for monoatomic gas f = 3

So Q = 1.7 x 8.3 x (5/3) 15.5 = 364.5 J

c) Q = ΔE + W

hence ΔE = Q - W = 145.8 J

d) Kinetic energy per atom = f K_{b} T/2

K_{b} = R/N_{a} , N_{a} is avogadro number
( 6.2 x 10^{23} )

so change in KE per atom ΔK = f K_{b} ΔT /2

= 3 x 8.3 15.5 / 2 x 6.2 x
10^{23} = 3.1x10^{-22} J

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