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(b)The pressure of the helium in the balloon is 100000 Pa. The volume of the balloon is 0.030m^3 The 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. __ New pressure= (2)

Question

(b)The pressure of the helium in the balloon is 100000 Pa.
The volume of the balloon is 0.030m^3
The 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.
__
New pressure=
(2)

(b)The pressure of the helium in the balloon is 100000 Pa. The volume of the balloon is 0.030m^3 The 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. __ New pressure= (2)

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OrsonElite · Tutor for 8 years

Answer

[120000 Pa]

Explain

## Step1: Recognize the problem type<br />The problem describes a change in the volume of a gas - helium in a balloon - that happens under constant temperature, with no gas entering or leaving the system. This is a case of Boyle's law in action, represented as \( P_1V_1=P_2V_2 \), wherein \( P_1 \) and \( V_1 \) denote initial pressure and volume, while \( P_2 \) and \( V_2 \) indicate final pressure and volume respectively.<br /><br />## Step2: Substitute given values into the formula<br />We are given the following variables: \( P_1=100000 \) Pa, \( V_1=0.030 \) \( m^3 \), and \( V_2=0.025 \) \( m^3 \).<br /><br />To calculate the unknown\( P_2 \), we insert these variables into Boyle's law and solve for \( P_2 \).<br /><br />### **The formula is given as:**<br />\( P_2= \frac {P_1 \cdot V_1}{V_2} \)<br /><br />### Insert the variables into the equation:<br />\( P_2= \frac {(100000 \mathrm{~Pa})*(0.030 \mathrm{~m}^{3})}{0.025 \mathrm{~m}^{3}} \)<br /><br />## Step3: Solve step-wise and verify <br />Do the calculation carefully. Multiply \( P_1 \) with \( V_1 \) to get \( P_1 \cdot V_1 = 3000 \) \( m^{3}Pa \).<br /><br />### Then divide with \( V_2 \) to get:<br />\( P_2= \frac{3000 \mathrm{~m}^{3}\mathrm{~Pa}}{0.025 \mathrm{~m}^{3}} = 120000 \mathrm{~Pa} \).
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