Recent content by rg2004

Homework Statement Show that I = log(u)-u+2log(v)-v is an invariant of the following system \dot{u}=u(v-2) \dot{v}=v(1-u) Homework Equations The Attempt at a Solution The question was given on a homework assignment, but I have very little idea what it is asking for and even...

So then would the derivative be \frac{d^2x}{dt^2t}=\frac{d}{dt}\frac{dx}{dt}=\frac{d}{dt}(v_0 \frac{dX}{dT})=\frac{d}{dT}(\frac{g}{v_0})(v_0 \frac{dX}{dT}) \frac{d^2x}{dt^2}=g\frac{d^2X}{dT^2} similarly \frac{d^2y}{dt^2}=g\frac{d^2Y}{dT^2} Thanks for your help

Homework Statement Consider a projectile subject to air resistance. The drag force is F=-\hat{v} C v^{a} where C and a are constants and v=\dot{r}. Restrict the problem to 2-D and take y in the vertical direction. Take the magnitude of initial velocity to be v_{0} and the initial position to...

Homework Statement Find the first 3 (non-zero) terms of the asymptotic series as x→∞ for ln(ex+1) Homework Equations ln(1+ε) ~ ε-ε2/2+ε3/3-O(ε4) (x→0) The Attempt at a Solution I found x+ln(1+e-x) (x→∞) = ln(ex+1) (x→∞) ε=e-x which allows me to use the Maclaurin series...

Alright, my best guess is that the system was disturbed and the temperature increased to 0 degrees C where it is in equilibrium.

What must be the final temperature if you have water and ice in equilibrium? -5 degrees Celsius apparently..

but isn't it also in equilibrium along the melting point line? To me, looking at the PT diagram indicates that the pressure must have gone up.

I'm sorry, I don't know heat balance equations. I've looked around, but I'm not sure which source to go by. Also I wouldn't know what to put for a change in temperature. Additionally, in equilibrium, I calculated that the pressure for this system is 649.3 atmospheres, and I don't know if any...

Homework Statement Supercooled water at minus 5C in a thermally insulated container suddenly transforms into an equilibrium ice-water mixture. a. What fraction of water has frozen? b. How much was the entropy change per gram? Homework Equations Clapeyron Equation...

perhaps I am supposed to assume that the gas is monoatomic? My textbook is vague and its not clear to me whether all ideal gasses are considered monoatomic. this is what i found: \gamma= 5/3 (ideal monatomic gas).

Homework Statement Suppose that one mole of an ideal gas expands in a quasi-static adiabatic process from P1 = 1 Pa and V1 = 1m3 to V2 = 8m3. What is the change in the pressure and the entropy of the gas? Homework Equations PV\gamma=constant The Attempt at a Solution I can't come...

Thanks!

I'd just like to check my answer, it seems too big Homework Statement Air initially at 20◦C is compressed by a factor of 15. What is the final temperature assuming that the compression is adiabatic and \gamma ≈ 1.4 the value of \gamma for air in the relevant range of temperatures? By what...

actually i found it. "if a divides bc, and a and b are coprime, then a divides c"

if 9 divides 2x does that imply 9 divides x? if so why? thanks