Question

One mole of an ideal gas expands isothermally and reversibly from 2 lit. to 20 lit. at 300 K. If the final pressure of the gas is 1 bar, the work done by the gas is

(a) -300R In10
(b) 300R In10
(c) 18
(d) -18

Answer 1

The work done by an ideal gas that expands isothermally and reversibly from 2 L to 20 L at 300 K is -300Rln10, corresponding to option (a).

Step-by-step explanation:

The question is about the calculation of the work done by an ideal gas that expands isothermally and reversibly. To find the work done (W), we can use the formula for isothermal expansion of an ideal gas, which is:

W = -nRTln(V2/V1)

Where:

• n is the number of moles of the gas
• R is the ideal gas constant
• T is the temperature in Kelvin
• V1 is the initial volume
• V2 is the final volume

Since the expansion is isothermal and the temperature (T) remains constant at 300 K:

• n = 1 mole (given)
• R = Ideal gas constant
• T = 300 K (given)
• V1 = 2 L (initial volume)
• V2 = 20 L (final volume)

Substituting these values into the equation:

W = -(1)(R)(300)ln(20/2) = -300Rln10

So, the work done by the gas is -300Rln10, which corresponds to option (a).