Verified Answer :

taskmasters

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 pressure and number of
moles of the gas the ratio T/V is equal to some constant. At another set of
condition of temperature, the constant is still the same. Calculations are as
follows:

T1 / V1 = T2 / V2

T2 = T1 x V2 / V1 

T2 = 25 x 3 / 2

T2 = 37.5 degrees Celsius

Answer : The new temperature will be, \(-74.4^oC\)

Explanation :

Charles' Law : This law states that volume of gas is directly proportional to the temperature of the gas at constant pressure and number of moles.

\(V\propto T\)     (At constant pressure and number of moles)

or,

\(\frac{V_1}{T_1}=\frac{V_2}{T_2}\)

where,

\(V_1\) = initial volume of gas = \(3.00m^3\)

\(V_2\) = final volume of gas = \(2.00m^3\)

\(T_1\) = initial temperature of gas = \(25^oC=273+25=298K\)

\(T_2\) = final temperature of gas = ?

Now put all the given values in the above formula, we get the final temperature of gas.

\(\frac{3.00m^3}{298K}=\frac{2.00m^3}{T_2}\)

\(T_2=198.6K=198.6-273=-74.4^oC\)

conversion used : \(^oC=K-273\)

Therefore, the temperature will be, \(-74.4^oC\)