Respuesta :
Answer:
[tex]T=-272.9^{o}C[/tex]
Explanation:
We have the ideal gasses equation [tex]PV=nRT[/tex] and the expression for the specific volume [tex]v=\frac{V}{m}[/tex], that is the inverse of the density, and for definition the number of moles is equal to the mass over the molar mass, that is [tex]n=\frac{m}{M}[/tex]
And we can relate the three equations as follows:
[tex]PV=nRT[/tex]
Replacing the expression for n, we have:
[tex]PV=\frac{m}{M}RT[/tex]
[tex]P\frac{V}{m}=\frac{RT}{M}[/tex]
Replacing the expression for v, we have:
[tex]Pv=\frac{RT}{M}[/tex]
Now resolving for T, we have:
[tex]T=\frac{PvM}{R}[/tex]
Now, we should convert all the quantities to the same units:
-Convert 500kPa to atm
[tex]500kPa*\frac{0.00986923}{1kPa}=4.93atm[/tex]
-Convert 0.2[tex]\frac{m^{3}}{kg}[/tex] to [tex]\frac{L}{kg}[/tex]
[tex]0.2\frac{m^{3} }{kg}*\frac{1L}{1m^{3}}=0.2\frac{L}{kg}[/tex]
- Convert the molar mass M of the water from [tex]\frac{g}{mol}[/tex] to [tex]\frac{kg}{mol}[/tex]
[tex]18\frac{g}{mol}=\frac{1kg}{1000g}=0.018\frac{kg}{mol}[/tex]
Finally we can replace the values:
[tex]T=\frac{(4.93atm)(0.2\frac{L}{kg})(0.018\frac{kg}{mol})}{0.082\frac{atm.L}{mol.K}}[/tex]
[tex]T=0.216K[/tex]
[tex]T=0.216K-273.15\\T=-272.9^{o}C[/tex]
