Respuesta :
Answer:
The volume of the gas becomes three times the initial volume.
Explanation:
Given that the pressure is constant, and temperature changes from -173degree C to 27degree C.
So, the initial temperature, [tex]T_1[/tex] = -173 degree C = -173+273 = 100 K.
The final temperature, [tex]T_2[/tex]= 27 degree C = 27+273=300 K.
As the pressure is constant, so [tex]P_1=P_2[/tex].
Let V_1 and V_2 be the initial and final volume respectively.
Assuming that the given gas is ideal gas.
So, applying the ideal gas equation
PV=nRT
where n is the number of moles of the gas and R is the universal gas constant.
For the initial state, [tex]P_1V_1=n_1RT_1\cdots(i)[/tex]
and for the final state, [tex]P_2V_2=n_2RT_2 \cdots(ii)[/tex]
Dividing the equation (i) by (ii), we have
[tex]\frac {P_1V_1}{P_2V_2}=\frac {n_1RT_1}{n_2RT_2} \\\\\frac {P_1V_1}{P_2V_2}=\frac {n_1T_1}{n_2T_2}[/tex]
As the mass of the gas is not changing, so [tex]n_1=n_2[/tex], then
[tex]\frac {P_1V_1}{P_2V_2}=\frac {T_1}{T_2}[/tex]
As the pressure is not changing, so [tex]P_1=P_2[/tex], then
[tex]\frac {V_1}{V_2}=\frac {100}{300}[/tex]
[tex]V_2=3V_1[/tex]
So, the volume of the gas becomes three times the initial volume.
