Question

A gas expands from an initial volume of 4.88 L to a final volume of 6.33 L against an external pressure of 810. mmHg. During the expansion the gas absorbs 10. J of heat. What is the change in the internal energy of the gas?

Answer 1

Given the amount of heat absorbed , q = +10 J

Work done by the system , W = -PV   ( -ve sign indicates that work is done by the system)

Where

P = external pressure = 810 mm Hg

   = 810 x 133.3 Pa                              Since 1 mm Hg = 133.3 Pa

= 107973 Pa

V = change in volume

       = final - initial volume

      = 6.33 - 4.88

     = 1.45 L

     = 1.45x10^-3 m³                Since 1 L = 10^-3 m³   

So W = -PV

        = - 156.6 J

According to first law of thermodynamics

q = E + W

So E = change in internal energy = q - W

            = 10 -(-156.6 ) J

           = 166.6 J

Therefore the change in the internal energy of the gas is 166.6 J