At a certain point in a pipe, air flows steadily with a velocity of \(150 \mathrm{m} / \mathrm{s}\) and has a static pressure of \(70 \mathrm{kPa}\) and a static temperature of \(4^{\circ} \mathrm{C}\). The flow is adiabatic and frictionless.

First, convert the given units into more workable ones. The static pressure is given in kiloPascals (kPa) but it is easier to work with Pascals (Pa), so convert it by multiplying by 1000. Likewise, convert the temperature from degrees Celsius to Kelvin by adding 273.15 to it. Thus, the static pressure becomes \(70,000 \, Pa\) and the static temperature \(277.15 \, K\).

Next, apply Bernoulli's equation, which states that the total energy in a steadily flowing fluid system is constant along the flow path. The formula is: \[\frac{1}{2}ρv^{2} + ρgh + p = constant\] where ρ is the fluid density, \(v\) is the fluid velocity, \(g\) is acceleration due to gravity, \(h\) is height, and \(p\) is pressure. Given that there are no height changes in the pipe and the flow has a constant velocity, the equation simplifies to: \[\frac{1}{2}ρv_{1}^{2} + p_{1} = \frac{1}{2}ρv_{2}^{2} + p_{2}\] where the subscript '1' refers to initial conditions and '2' refers to final conditions. As velocities are constant, the final pressure \(p_{2}\) becomes: \(p_{2}=p_{1}-\frac{1}{2}ρ(v_{1}^{2}-v_{2}^{2})\). Here, it's given that the flow is adiabatic and frictionless, meaning there are no changes in velocity, so \(v_{1} = v_{2}\). Therefore, the pressure remains constant.

The change in temperature can be determined using the ideal gas law which states that the pressure of a gas is directly proportional to its temperature if the volume and quantity of gas are held constant, written as \(p=ρRT\), where \(R\) is the specific gas constant. Isolated and substituting in the adiabatic, inviscid flow conditions where pressure \(p\) is constant this equation rewrites as \(T_{2}=T_{1}\), which indicates, that the temperature remains constant as well.