Select the balloon volume that would represent the following conditions: the temperature is increased by half while the pressure is simultaneously decreased by half.

Answer 1

Assuming the amount of gas stays constant, the combined gas law can be used to determine the final volume of the balloon:

\( \frac{P_1 \times V_1}{T_1} = \frac{P_2 \times V_2}{T_2} \)

Let's assume the initial conditions are:
- Pressure (P1) = 1 atm
- Volume (V1) = 1 L
- Temperature (T1) = 1

After applying the changes:
- Pressure (P2) = 0.5 atm (half of the initial pressure)
- Temperature (T2) = 1.5 (half more of the initial temperature)

Now, we need to solve for the final volume (V2):
\( \frac{1 \times 1}{1} = \frac{0.5 \times V_2}{1.5} \)

\( V_2 = \frac{1 \times 1.5}{0.5} = 3 \)

So, the final volume of the balloon would be 3 L.