Question

As a bicycle pump inflates a tyre, it pressure rises from 30 kPa to 40 kPa at constant temperature of 30 °C. By assuming the air acts as an ideal gas, calculate the work done per mol of the air.
A. -80.35 J
B. 80.35 J
C. -811.93 J
D. 811.93 J
(please show calculation)
can use this formula W=nRT ln(p1/p2)​

Answer 1

This question involves the concepts of work done, pressure, and temperature.

The work done per mol of the air is "-724.71 J/mol".

Using the given formula for work done:

$W=RTln\frac{P_1}{P_2}$

where,

W = work done per mol = ?

R = universal gas constant = 8.314 J/mol.k

T = absolute temperature = 30°C + 273 = 303 k

P₁ = initial pressure = 30 KPa

P₂ = final pressure = 40 KPa

Therefore,

$W= (8.314\ J/mol.k)(303\ k)ln\frac{30\ KPa}{40\ KPa}$

W = -724.71 J/mol

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