Calculate the change in temperature that would shrink a room-temperature balloon to one-half its size. Vo is 10 Vf is 5
P V = n R T
V and T change
P stays constant - 1 atmosphere
n stays constant, same molecules in there
R just plain is a constant
so
T = constant * V
V2 = .5 V1
T1 = constant * V1
T2 = constant * .5 V1 = constant * .5 T1
half the volume is half the temperature
if the original temp was 20 C that is 293 K
so the final temp is 146 K or -127 C
okay ... 20ºC ... or 293ºK
gas volume is proportional to the absolute (Kelvin) temperature
so half of the ambient temperature is the change required
room temp is 20 C right?
so using Charles' law
To calculate the change in temperature that would shrink a balloon to one-half its size, we can use the ideal gas law. The ideal gas law relates the pressure, temperature, volume, and number of moles of a gas. It is represented by the formula:
PV = nRT
Where:
P is the pressure of the gas
V is the volume of the gas
n is the number of moles of the gas
R is the ideal gas constant
T is the temperature of the gas
Given:
Vo = 10 (initial volume)
Vf = 5 (final volume)
Since we know the initial and final volumes of the balloon, we can set up the following equation:
(Vo/Vf) = (Tf/To)
Where:
To is the initial temperature
Tf is the final temperature
By rearranging the equation, we can solve for Tf:
Tf = To * (Vf / Vo)
Now let's substitute the given values into the equation:
Tf = To * (5/10)
Simplifying further:
Tf = 0.5To
Therefore, the final temperature (Tf) needed to shrink the balloon to one-half its size is half of the initial temperature (To).