Question

the pressure of the helium in the balloon is 100,000 Pa. The volume of the balloon is 0.030m ^3. Balloon is compressed at a constant temperature causing the volume to decrease to 0.025m^3. No helium leaves the balloon. Calculate the new pressure in the balloon

Answer 1

Since the temperature and mass of the gas is constant during the process, and helium can be considered as ideal gas, we can apply the Boyle–Mariotte law (see https://en.wikipedia.org/wiki/Boyle%27s_law):

$$P_1V_1 = P_2V_2$$

where $P_1 = 100000Pa, V_1 = 0.030m^3$ are the pressure and volume before the compression respectively, and $P_2, V_2 = 0.025m^3$ are the pressure and volume after the compression respectively. Thus, expressing $P_2$, obtain:

$$P_2 = \dfrac{P_1V_1}{V_2}\\ P_2 = \dfrac{100000Pa\cdot 0.030m^3}{0.025m^3} = 120000Pa$$

Answer. 120000 Pa.