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 10²³ )

so change in KE per atom ΔK = f K_b ΔT /2
   = 3 x 8.3 15.5 / 2 x 6.2 x 10²³  = 3.1x10^-22 J