Question

A sample of a low-density gas is initially at room temperature and has pressure p. The gas is warmed at constant volume until the pressure is 2p. Compared to the initial Celsius temperature of the gas, the final Celsius temperature is

Answer 1

Answer:

Compared to the initial Celsius temperature of the gas, the final  Celsius temperature is  greater by a factor of more than 2.

Explanation:

Gay-Lussac's law states that the pressure of a fixed volume of a gas is directly proportional to its temperature. In other words, if the temperature increases, the pressure will increase and if the temperature decreases, the pressure will decrease.

In summary, Gay-Lussac's law is a law that says that when the amount of gas and volume are kept constant, the quotient that exists between the pressure and the temperature will always have the same value:

$\frac{P}{T}=k$

Being an initial state 1 and a final state 2, it is true:

$\frac{P1}{T1} =\frac{P2}{T2}$

In this case:

• P1= p
• T1= t
• P2= 2p
• T2= ?

Replacing:

$\frac{p}{t} =\frac{2p}{T2}$

Solving:

$T2=2p*\frac{t}{p}$

T2= 2*t

Compared to the initial Celsius temperature of the gas, the final  Celsius temperature is  greater by a factor of more than 2.