a) Write a formula for the total differential of the volume of an ideal gas as a function of (T,P). Divide this by V and show that dV/V=(dT/T)(dP/P) (this demonstrates that increasing the temperature by dT has the same fractional effect on the volume as decreasing the pressure by dP ). b) Using similar steps, derive a similar formula for the total differential of the volume of a cylinder with variable radius =r and height =h