Can someone help me with this ideal gass law problem?
One method of estimating the temperature of the center of the sun is based on the assumption that the center of consists of gases that have an average molar mass of 2 g/mol. If the density of the center of the sun is 1.40 g.cm^3 at a pressure of 1.30*10^9 atm, calculate the temperature. Answer in units of celsius.
I would really like an explantion on the process on finding an answer to this question. Thank you.
Lets assume that the gas on the sun can be considered as a ideal gas. So we can use ideal gas law to this.
PV = nRT
P = pressure in pascal
V = volume in cubic meter
n = amount of moles
R = universal gas constant
T = temperature in kelvin
But we know that;
density(`rho`) = mass(m)/volume(V) ---> `rho` = m/V
moles(n) = mass(m)/molar mass(M) ---> n = m/M
`PV = nRT`
`PV = (m/M)RT`
`P = (m/V)(RT)/M`
`P = rho (RT)/M`
`T = (MP)/(Rrho )`
M = 2 g/mol = `2xx0^-3` kg/mol
P = `1.3xx10^9` atm
R = 0.08206 LatmK/mol
`rho` = 1.4 g/cm^3 = 1.4xx10^-3/10^-3 = 1.4 kg/L
T = `(2xx1.3xx10^9)/(0.08206xx1.4)`
T = `2.263xx10^10` K
T = `2.263xx10^10-273.15` C
T = `2.263xx10^10` C
Since the temperature is very high there is no difference in temperature of Kelvin and Celsius.
So the temperature on the sun is `2.263xx10^10` C.