Question

A cylinder of volume 0.290 m^{3} 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 m^{3}. 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
m^{3}.

J

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

J

(g) Compute Δ*U* − *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*, Δ*U*, 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**

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