Obtain expressions for the isothermal compressibility k =(-1/v)(dv/dp)t for: (a) an ideal gas, and (b) for a van der waals gas, (c) show that in the limit v goes to (infinity) the isothermal compressibility of the van der waals gas is the same as that of an ideal gas.

Write short note on the following ; collision theory, rotation angle and angular velocity, centripetal acceleration, coriolis force, and newton's law of gravitation.

When a 5.0kg cart undergoes a 2.2m/s increase in speed, what is the impulse of the cart

Asheet of steel 1.5 mm thick has nitrogen atmospheres on both sides at 1200oc and is permitted to achieve a steady-state diffusion condition. the diffusion coefficient for nitrogen in steel at this temperature is 6 x 10- 11 m2 /s, and the diffusion flux is found to be 1.2 x 10-7 kg/m2 -s. also, it is known that the concentration of nitrogen in the steel at the high-pressure surface is 4 kg/m3 . how far into the sheet from this high-pressure side will the concentration be 2.0 kg/m3 ? assume a linear concentration profile.