- #1
thinkingcap81
- 27
- 2
I'd like to apply the 1st law of thermodynamics in a reference frame (RF) moving with constant velocity. We have:
##\Delta{}E = E_{in} - E_{out}##
I am limiting myself to rectilinear motion.
Suppose we are in a RF moving with a constant velocity ##V##.
Let the system consist of a mass ##m##. The absolute and relative velocities of ##m## are ##V_a## and ##V_r## with ##V_a = V + V_r##.
We burn a fuel releasing energy ##Q## which is completely utilized to do work on the mass ##m##. All this work goes into increasing the velocity of ##m##.
The absolute velocity of ##m## changes from ##V_{a1}## to ##V_{a2}##. The relative velocity of ##m## changes from ##V_{r1}## to ##V_{r2}##.
The change in kinetic energy (KE) as measured in the fixed and moving RFs are:
##\Delta{}KE_a = \frac{1}{2}m\left(V^2_{a2} - V^2_{a1}\right)## and ##\Delta{}KE_r = \frac{1}{2}m\left(V^2_{r2} - V^2_{r1}\right)##
Thus we have: ##\Delta{}KE = Q##.
I think that we measure identical ##Q## in both stationary and moving RFs. But ##\Delta{}KE_a \ne \Delta{}KE_r##.
So where am i going wrong?
##\Delta{}E = E_{in} - E_{out}##
I am limiting myself to rectilinear motion.
Suppose we are in a RF moving with a constant velocity ##V##.
Let the system consist of a mass ##m##. The absolute and relative velocities of ##m## are ##V_a## and ##V_r## with ##V_a = V + V_r##.
We burn a fuel releasing energy ##Q## which is completely utilized to do work on the mass ##m##. All this work goes into increasing the velocity of ##m##.
The absolute velocity of ##m## changes from ##V_{a1}## to ##V_{a2}##. The relative velocity of ##m## changes from ##V_{r1}## to ##V_{r2}##.
The change in kinetic energy (KE) as measured in the fixed and moving RFs are:
##\Delta{}KE_a = \frac{1}{2}m\left(V^2_{a2} - V^2_{a1}\right)## and ##\Delta{}KE_r = \frac{1}{2}m\left(V^2_{r2} - V^2_{r1}\right)##
Thus we have: ##\Delta{}KE = Q##.
I think that we measure identical ##Q## in both stationary and moving RFs. But ##\Delta{}KE_a \ne \Delta{}KE_r##.
So where am i going wrong?