Question

You are toying with a tire pump and block the exit valve completely. With it blocked, you compress the pump isothermally at 300K from an initial volume of 0.6 L to a final volume of 0.3 L. Taking the gas inside the pump to be ideal, and its initial pressure to be 1 atm = 1.013 x105 Pa, what is the work done (in Joules) by the gas during your compression?

Answer 1

Work done by gas in isothermal process
W = nRT ln(Vf/Vi) (n is number of moles of gas, R is gas constant T is absolute temperature of gas Vi and Vf are initial and final volume of gas)

By ideal gas equation PV = nRT
P is gas pressure and V is it's volume
Hence work done
W = PiVi ln(Vf/Vi)    or PfVf ln(Vf/Vi)   ( as temperature is constant PV remains constant during compression)
W = 1.013x105 Pa * 0.6x10-3 m3 ln(0.3 ltr / 0.6 ltr)
   = - 42.13 J