To solve this we assume that the gas inside the balloon is an ideal gas. Then, we can use the ideal gas equation which is expressed as PV = nRT. At a constant volume pressure and number of moles of the gas the ratio of T and P is equal to some constant. At another set of condition, the constant is still the same. Calculations are as follows:
T1/P1 = T2/P2
P2 = T2 x P1 / T1
P2 = 25 x 29.4 / 75
P2 = 9.8 kPa
Answer : The new pressure of gas will be, 25.176 kPa
Solution :
Gay-Lussac's Law : It is defined as the pressure of the gas is directly proportional to the temperature of the gas at constant volume and number of moles.
[tex]P\propto T[/tex]
or,
[tex]\frac{P_1}{T_1}=\frac{P_2}{T_2}[/tex]
where,
[tex]P_1[/tex] = initial pressure of gas = 29.4 kPa
[tex]P_2[/tex] = final pressure of gas = ?
[tex]T_1[/tex] = initial temperature of gas = [tex]75^oC=273+75=348K[/tex]
[tex]T_2[/tex] = final temperature of gas = [tex]25^oC=273+25=298K[/tex]
Now put all the given values in the above equation, we get the final pressure of gas.
[tex]\frac{29.4kPa}{348K}=\frac{P_2}{298K}[/tex]
[tex]P_2=25.176kPa[/tex]
Therefore, the new pressure of gas will be, 25.176 kPa
