Answer:
3. doubles
Explanation:
for an ideal gas behavior, the relationship between volume and temperature is given by Charles law
Charles law states that the volume of a given mass of gas is directly proportional to its temperature provided that pressure remains constant. Mathematically, this is represented as
V ∝ T
V=KT
K = V/T
where V is the volume of the gas
T is the Temperature
k represents the constant of proportionality
For initial and final conditions of a gas,
[tex]\frac{V_{1} }{T_{1} }[/tex] = [tex]\frac{V_{2} }{T_{2} }[/tex]
where 1 and 2 represent initial and final conditions respectively
therefore, T₁ = 100 and T₂ = 200
[tex]\frac{V_{1} }{100}[/tex] = [tex]\frac{V_{2} }{200}[/tex]
200 × V₁ = 100 × V₂
divide both sides by 100
2V₁ = V₂
final volume,V₂ = 2V₁
there the volume doubles
The increase in temperature results in the volume of the gas to be doubled. Hence, option 3 is correct.
The ideal gas relationship with volume and temperature at constant pressure has been given by Charles law. The relation has been expressed as:
[tex]\dfrac{V_1}{T_1} =\dfrac{V_2}{T_2}[/tex]
Where the initial volume of gas, [tex]V_1[/tex]
The final volume of gas, [tex]V_2[/tex]
The initial temperature of gas, [tex]T_1=100^\circ \rm C[/tex]
The final temperature of gas, [tex]T_2=200^\circ \rm C[/tex]
Substituting the values for relation between volume has been given as:
[tex]\dfrac{V_1}{100} =\dfrac{V_2}{200}\\V_2=\dfrac{V_1}{100} \;\times\;200\\V_2=2\;V_1[/tex]
The final volume gas has been double the initial volume. Thus, with increase in temperature the volume of the gas as been doubled. Hence, option 3 is correct.
For more information about ideal gas, refer to the link:
https://brainly.com/question/8711877
