Question

A helium-filled toy balloon has a gauge pressure of 0.350 atm and a volume of 8.0 liters. How much greater is the internal energy of the helium in the balloon than it would be at zero gauge pressure?__________J

Please show all work to get credit.

Answer 1

You cannot solve this problem using the work. Because the volume does not change no work is done.

To solve this problem remember that the internal of an ideal gas is given by:
U = n?Cv?T

The specific heat capacity Cv for a monatomic ideal gas like helium is
Cv = (3/2)?R

Hence:
U = (3/2)?n?R?T

Using ideal gas law you can express internal energy in terms of volume and pressure:
p?V = n?R?T
=>
U = (3/2)?p?V

So the internal energy difference between two states1 and 2 is:
?U = (3/2)?(p??V? - p??V?)

Since Volume is the same, i.e. V? = V? = V
?U = (3/2)?(p? - p?)?V = (3/2)??p?V

Generally you should use absolute pressure and absolute temperature in thermodynamic calculations. Only in the special case of algebraic differences (?p or ?T) you can use shifted units of measurement like gauge pressure or Celsius temperature, because the shift factor cancels out, e.g.:
?U = (3/2)?((p_gauge? + p_atm) - (p_gauge? + p_atm))?V
= (3/2)?(p_gauge? - p_gauge?)?V
= (3/2)??p_gauge?V

But if you want to calculate internal energy of each state from
U = (3/2)?p?V
you must use absolute pressure.

Moreover you need to convert pressure to Pascals and Volume to cubic meters in order to obtain result in Joules (1 J = 1Pam