Question

A thermodynamic system consists of an ideal gas at an initial volume of 2.90 L and a pressure of 7.1 × 104 Pa. An external force performs 170 J of work as it compresses the gas at constant pressure. What is the new volume of the gas?

5.3l
0.51l

Answer 1

The initial volume of the gas is (keeping in mind that
`1.0 L= 1 \cdot 10^(-3) m^3`):

`V_i = 2.90 L= 2.90 \cdot 10^(-3)m^3`

The work done by the external force on the gas is

`W= -p \Delta V=-p (V_f - V_i)= -pV_f + pV_i`
where p is the pressure and
`V_f` the final volume. Re-arranging this equation, we can find the final volume Vf:

`V_f = V_i - (W)/(p)=2.90 \cdot 10^(-3) m^3 - (170 J)/(7.1 \cdot 10^4 Pa) =0.5 \cdot 10^(-3) m^3 = 0.5 L`
and this value makes sense, because it is less than the initial volume of the gas, in fact the problem says that the external force compresses the gas.