Solution:

Given that density \(\rho\) is constant, we use the ideal gas law:

\[
\frac{P}{T} = \text{constant (since } \rho \text{ is constant)}
\]

If the temperature \(T\) is doubled, then:

\[
\frac{P_2}{T_2} = \frac{P_1}{T_1} \Rightarrow \frac{P_2}{2T_1} = \frac{P_1}{T_1}
\]

Thus, \(P_2 = 2P_1\), meaning the pressure also doubles, resulting in a 100% increase.