An ideal gas undergoes an adiabatic process and does 25 joules of work on its environment. what is the change in internal energy? a.50 joules b. 25 joules c. 0 joules d. -25 joules

Space-time metric ds2= -dt2+at2dx2+bt2dy2+ct2dz2 (a)how does the area of a rectangle with vertices at ( x=0, y=0, z=0 ), (1,0,0 ), ( 0,1,0 ) and (1,1,0 ) changes with time? (b) if a photon moving in the x direction starts from the origin at t=1, when does it reach x=l? (ds=0 for the trajectory of a photon.) (c) the proper time for a particle is defined by cd=ds. what is the proper time for a particle to move along the trajectory ( x(t)=t, y(t)=0, z(t)=0 ) from t=0 to 1 ? what is the condition on the parameter a so that the velocity of the particle never exceeds the speed of light ?

Adiver named jacques observes a bubble of air rising from the bottom of a lake (where the absolute pressure is 3.50 atm) to the surface (where the pressure is 1.00 atm). the temperature at the bottom is 4.00 ∘c, and the temperature at the surface is 23.0 ∘c.what is the ratio of the volume of the bubble as it reaches the surface (vs) to its volume at the bottom (vb)? if jaques were to hold his breath the air in his lungs would be kept at a constant temperature. would it be safe for jacques to hold his breath while ascending from the bottom of the lake to the surface?

Currents in dc transmission lines can be 100 a or higher. some people are concerned that the electromagnetic fields from such lines near their homes could pose health dangers. for a line that has current 150 a and a height of 8.0 m above the ground, what magnetic field does the line produce at ground level? express your answer in teslas and as a percentage of the earth’s magnetic field, which is 0.50 g. is this value cause for worry?