For a reversible adiabatic ideal gas expansion dp÷p is equal to

To solve this problem, we need to use the equation for a reversible adiabatic process for an ideal gas. The equation is given by:

dp/p = -γ dV/V

Where dp is the change in pressure, p is the initial pressure, dV is the change in volume, V is the initial volume, and γ is the heat capacity ratio.

Step 1: Identify the given information in the problem statement. In this case, we are given that the process is reversible and adiabatic.

Step 2: Recall the equation for a reversible adiabatic process for an ideal gas: dp/p = -γ dV/V

Step 3: Substitute the given information into the equation. Since the process is adiabatic, there is no heat transfer, so γ = Cp/Cv, where Cp is the specific heat at constant pressure and Cv is the specific heat at constant volume.

Step 4: Simplify the equation. Since the process is reversible, we can assume that the initial and final states of the gas are in equilibrium, so the equation becomes:

dp/p = -γ dV/V

Step 5: Solve for dp/p. Rearrange the equation to isolate dp/p:

dp/p = -γ dV/V

Step 6: Simplify the equation further if necessary. If there are any known values for γ, p, and V, substitute them into the equation to find the value of dp/p.

Step 7: Calculate the value of dp/p. Use the given values and any known values to calculate the value of dp/p.

Step 8: Write the final answer. The value of dp/p is equal to the calculated value from step 7.

In summary, to find the value of dp/p for a reversible adiabatic ideal gas expansion, follow the steps outlined above.