Answer
The correct diagram is the one labeled "2".
Work Step by Step
1. Write the combine gas law:
$\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$
2. If the atmospheric pressure is doubled: $P_2 = 2P_1$
3. If the Kelvin temperature is doubled: $T_2 = 2T_1$
4. Substitute these equations into the combined gas law:
$\frac{P_1V_1}{T_1} = \frac{(2P_1)V_2}{(2T_1)}$
- Multiply both sides by "$T_1$":
$P_1V_1 = \frac{2P_1V_2}{2}$
- 2 divided by 2 equals to 1.
$P_1V_1 = P_1V_2$
- Divide both sides by "$P_1$"
$V_1 = V_2$
5. Therefore, the final volume is equal to the initial one. The diagram $2$ represents exactly this situation.
