A helium-filled toy balloon has a gauge pressure of 0.250 atm and a volume of 8.0 liters.
How much greater is the internal energy (in J) of the helium in the balloon than it would be at zero gauge pressure?

The internal energy of the gas is 1.25 times greater when the helium is at 0.250 atm gauge pressure.

Explanation:

Since the helium in the balloon is an ideal gas, we can use the equation of state for ideal gases:

where

p is the pressure

V is the volume

n is the number of moles

R is the gas constant

T is the absolute temperature of the gas

For the helium gas in the balloon, we have:

(the total pressure is sum of the gauge pressure + atmospheric pressure)

is the volume

So we can write the temperature as

Instead, when the helium balloon is at zero gauge pressure (=at atmospheric pressure), we have

Therefore, the temperature would be

The ratio between the two temperatures is

And we also know that the internal energy of a gas is directly proportional to the temperature:

Therefore, the internal energy of the gas is 1.25 times greater when the helium is at 0.250 atm gauge pressure.

0.93xc=0.93x3x10^8m/s

2.54cm is 1 inch

360seconds i 1 hr

one "light year" is the distance that light travels, through vacuum, in one julian year.   that's 365.25 days, of 24 hours each.