Question

A cylinder of volume 0.290 m³ contains 11.9 mol of neon gas at 17.3°C. Assume neon behaves as an ideal gas.

(a) What is the pressure of the gas?
Pa

(b) Find the internal energy of the gas.
J

(c) Suppose the gas expands at constant pressure to a volume of 1.000 m³. How much work is done on the gas?
J

(d) What is the temperature of the gas at the new volume?
K

(e) Find the internal energy of the gas when its volume is 1.000 m³.
J

(f) Compute the change in the internal energy during the expansion.
J

(g) Compute ΔU − W.
J

(h) Must thermal energy be transferred to the gas during the constant pressure expansion or be taken away?

This answer has not been graded yet.

(i) Compute Q, the thermal energy transfer.
J

(j) What symbolic relationship between Q, ΔU, and W is suggested by the values obtained?

Answer 1

given
V1 = 0.290 m^3
n = 11.9 mol
T1 = 17.3 C
= 17.3 + 273

= 290.3 K

a) use, P*V = n*R*T

P = n*R*T/V

= 11.9*8.314*290.3/0.29

= 9.90*10^4 pa

b) Ui = (3/2)*n*R*T

= (3/2)*11.9*8.314*290.3

= 4.308*10^4 J

c) W = P*(V2 - V1)

= 9.90*10^4*(1 - 0.29)

= 7.03*10^4 J

d) at constant pressure, V2/T2 = V1/T1

T2 = (V2/V1)*T1

= (1/0.29)*290.3

= 1001 K

e) Uf = (3/2)*n*R*T2

= (3/2)*11.9*8.314*1001

= 1.486*10^5 J

f) delta_U = (3/2)*n*R*(T2 - T1)

= (3/2)*11.9*8.314*(1001 - 290.3)

= 1.05*10^5 J

g) delta_U - W = 1.05*10^5 - 7.03*10^4

= 3.47*10^4 J

h) Heat energy must be transfred to the gas

i) Q = W + delta_U

= 7.03*10^4 + 1.05*10^5

= 1.75*10^5 J

j) Q = delta_U + W