I am assuming that B is a stationary observer here.
For the first part of the trip, using the formula, rocket A is approaching B at velocity $$v_A$$ =0.6 c.
The length that A travels is $$L_A = v_A t_1 $$ where $$t_1 = $$ 6 hrs. For the first part of the trip, B is receiving signals at a rate...
I did it in the first case so that
$$x_2'-x_1' = \gamma (x_2 - x_1 - v (t_2 - t_1) = \gamma D \because t_2 - t_1 = 0 $$ but the final answer impliesthat $$t_2-t_1 = \frac{D}{c} $$
In relation to the attached diagram, I described the position of ##x_1, x_2 ## and hence took their difference, and transformed it to the primed reference frame where ##t' = ## constant
Oh so actually it's ## t'_1 = t'_2 ##, so in that case, ##x_2-x_1 = D + c(t_2 - t_1 ) ## as both sources would emit light simultaneously and hence
$$x_2'-x_1' = \gamma (D + c(t_2 - t_1) - v(t_2 - t_1)$$ and since in O', the event is simultaneous, I got
$$t_2'-t_1' = 0 = \gamma \[ t_2 - t_1 -...
Why do I need ##t'## coordinates if I am only considering the length difference in O' ? Furthermore in O, how does the time difference of ##\frac{D}{c}## emerge if both events are simultaneous in O.
I let E1 be the event where source 1 emits the photon and E2 for the second source with the respective coordinates in O as $(x_1, t_1$) and $(x_2,t_2)$ such that $t_2=t_1 \because$ simultaneous and $x_2-x_1 =D$.
Using Lorentz transformation I obtained that in O', $$x'_2-x'_1 = \gamma...
The solutions start from the fact that c_v= (dT/dV)_s = -[(du/dv)_T + P], however I cannot reason where did that come from. Any help will be appreciated.
I proceeded, then differentiated wrt P and got that f'(P) = (T^3/P^2)(b/3 -a ).
Hence I proved that b/3 -a must be zero by contradiction as otherwise f would be a function of T and P.
Hence a/b = 1/3, and f'(T) = 0 so that f'(T) is come constant.
Initial conditions would be V_0 P_0 and T_0...
Starting from v(P,T),
dv=(dv/dp)_T dp + (dv/dT)_P dt
i implemented conditions when T and P are constant and ended up with
ln V = aT^3/P + constant and ln V = bT^3 /3P + constant
If i assume that the constant is 0, i can say that a/b = 1/3 but how do i justify this assumption?
Should I assume that the partial derivative of P wrt T remains constant throughout the process or that the specific volume of ice remains constant to work out the graph of P vs T for solid phase? Thanks.