Question

A balloon is inflated to its full extent by heating the air inside it. The volume of the balloon changes from 4.00 × 10⁶ L to 4.50 × 10⁶ L by the addition of 1.3 × 10⁸ J of heat. Assuming the balloon expands against a pressure of 1.0 atm, calculate the ∆E (in J) of the process. 1 L･atm=101.3 J.

Answer 1

∆E = 7.9 × 10⁷ J

Step-by-step explanation:

The air absorbs 1.3 × 10⁸ J of heat (Q), that is, Q = 1.3 × 10⁸ J.

The work (W) done by the expansion of the gas can be calculated using the following expression.

W = -P . ∆V

where,

P is the external pressure

∆V is the change in the volume

`W=-P.\Delta V=-1.0atm * (4.50 * 10^(6)L- 4.00 * 10^(6)L) *(101.3J)/(1L.atm) =-5.1 * 10^(7)J`

The change in the internal energy (∆E) can be calculated using the following expression.

∆E = Q + W

∆E = 1.3 × 10⁸ J + (-5.1 × 10⁷ J) = 7.9 × 10⁷ J