Answer :
The gas temperature change if the volume is halved and the pressure is tripled by factor 6.
What is an ideal gas?
An ideal gas is theoretical gas composed of many randomly moving point particles that are not subject to interparticle interactions. The ideal gas concept is useful because it obeys ideal gas law, a simplified equation of state, and is amenable to analysis under statistical mechanics.
Considering combined law equation:
Temperature increases by factor of 6.
Gay-Lussac's Law
Gay-Lussac's Law indicates that, as long as volume of the container containing the gas is constant, as the temperature increases, the gas molecules move faster. Then number of shocks against the walls increases, that is, the pressure increases. That is, gas pressure is directly proportional to its temperature.
In summary, when there is constant volume, as the temperature increases, the gas pressure increases. And when temperature decreases, gas pressure decreases.
Gay-Lussac's law can be expressed as mathematically as follows:
where:
P= pressure
T= temperature
k= Constant
Boyle's Law
Pressure and volume are related by Boyle's law, which says that volume occupied by a given mass of gas at constant temperature is inversely proportional to pressure.
Boyle's law is expressed mathematically as follows:
P× V=k
where:
P= pressure
V= volume
k= Constant
Charles's Law
Finally, Charles's Law consists of the relationship that exists between the volume and the temperature of certain amount of ideal gas, which is maintained at a constant pressure.
This law says that for given sum of gas at constant pressure, as the temperature increases, the volume of the gas increases and as the temperature decreases, the volume of the gas decreases. That is, volume is directly proportional to the temperature of the gas.
In summary, Charles' law is a law that says that when amount of gas and pressure are kept constant, the ratio between volume and temperature will always have the same value:
where:
V= volume
T= temperature
k= Constant
Combined law equation
Combined law equation is combination of three gas laws called Boyle's, Charlie's and Gay-Lussac's law:
Studying the two different states, an initial state 1 and an final state 2, the following will be true:
In this case, you know that:
Volume is double: V2= 2×V1
Pressure is tripled: P2= 3×P1
So, replacing in combined law equation:
Solving:
T2= 6×T1
Finally, temperature increases by a factor of 6.
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