During an isothermal process on an ideal gas, the pressure rises by...

For an isothermal process on an ideal gas, the product of pressure and volume is constant.

$PV = \text{constant}$

Differentiating both sides, we get:

$P \, dV + V \, dP = 0$

$\dfrac{dV}{V} = -\dfrac{dP}{P}$

Multiplying by $100$ to get the percentage change:

$\dfrac{dV}{V} \times 100 = - \left(\dfrac{dP}{P} \times100\right)$

Given that the pressure rises by $0.5\%$, we have $\dfrac{dP}{P} \times100 = 0.5\%$.

$\dfrac{dV}{V} \times100 = -0.5\%$

The negative sign indicates a decrease in volume. Therefore, the volume decreases by approximately $0.5\%$.