   Chapter 12, Problem 14P

Chapter
Section
Textbook Problem

A cylinder of volume 0.300 m3 contains 10.0 mol of neon gas at 20.0°C. Assume neon behaves as an ideal gas. (a) What is the pressure of the gas? (b) Find the internal energy of the gas. (c) Suppose the gas expands at constant pressure to a volume of 1.000 m3. How much work is done on the gas? (d) What is the temperature of the gas at the new volume? (e) Find the internal energy of the gas when its volume is 1.000 m3. (f) Compute the change in the internal energy during the expansion. (g) Compute ΔU − W. (h) Must thermal energy be transferred to the gas during the constant pressure expansion or be taken away? (i) Compute Q, the thermal energy transfer. (j) What symbolic relationship between Q, ΔU, and W is suggested by the values obtained?

(a)

To determine
The pressure of the gas.

Explanation

Given Info:

The volume of the cylinder is 0.3m3 .

The amount of neon gas in the cylinder is 10mol .

The initial Temperature of the gas is 20°C .

For an ideal gas, PV=nRT .

Formula to calculate the pressure of the gas is,

Pi=nRTiVi

• n is the amount of gas in moles
• R is the universal gas constant
• Ti is the initial temperature
• Vi is the initial volume

Substitute 10mol forn, 8.31J/molK for R, 20°C for Ti and 0

(b)

To determine
the internal energy of the gas.

(c)

To determine
the work done on the gas in expansion at constant pressure.

(d)

To determine
the temperature of the gas at new volume.

(e)

To determine
the internal energy of the gas when its volume is 1m3 .

(f)

To determine
the change in internal energy during the expansion.

(g)

To determine
the value of ΔUW .

(h)

To determine
whether the thermal energy is transferred into the gas or taken away from the gas during the expansion.

(i)

To determine
the thermal energy transferred.

(j)

To determine
the relationship between Q, W and ΔU .

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