course Phy 202
Very good questions. See my notes and see if they help. If not, you may of course ask additional questions.
I am still working on these Ch.13 problems - #17 What is the fractional change in density of a lead sphere whose temp decreases from 25*C to -40*C? You told me that density is mass/volume and to assume that initial volume V1, mass m. And that m/V1=rho1, where rho is the original density. Do I use 'drho=-beta(rho)('dt) to solve this? The density of lead is 11.3x10^3 kg/m^3, and the volume of a sphere is 4/3pir^3. I don't know mass and need either it or volume to solve rho=m/v. I am confused and don't know where to go from here.
Density is mass / volume.
The change in volume is
`dV = beta rho V_1 `dT,
where V_1 is the original volume of the substance.
So rho_1 = m / V_1, and
rho_2 = m / V_2,
where V_2 is the new volume: V_2 = V_1 + `dV = V_1 + beta rho V_1 `dT.
So we have
`drho = `rho_2 - `rho_1 = m / V_2 - m / V_1, where
m = rho_1 * V0.
Substitute rho_1 * V0 for m in `drho = m / V_2 - m / V_1, then do the algebra to simplify the resulting expression.
I also have a question about #48 By what factor will the rms speed of gas molecules increase if the temp is increased from 0*C to 100*C? Vrms=sqrt(3KT/m) but I am not given m for this problem. I need to know the Vrms for each to determine the factor by which it increases. I am stuck at this point.
m is the same at both temperatures, so if you divide sqrt(3K T1 /m) by sqrt(3K T2 /m), the m's will cancel. As will a lot of other stuff, leaving you a ratio that depends only on the two temperatures.
Finally #55 What is the rms speed of nitrogen molecules contained in an 8.5-m^3 volume at 2.1atm if the total amount of nitrogen is 1300mol? In order to solve this problem for Vrms=sqrt(3KT/m) I need the temp - is this the correct way to approach this problem or do I need to go another way? Please Help!!
You can use PV = n R T with the given information to find the temperature.