The present paper describes the design of a new adiabatic flow calorimeter which is capable of measuring the integral Joule-Thomson effect and the isobaric enthalpy increment in the gaseous phase. The underlying principles for calorimetric measurements are discussed, and the measuring devices are described. Heat losses were shown to be significantly less than the experimental accuracy. A theoretical maximum error calculation yielded values within the bounds of 0.9 per cent for the isobaric enthalpy increment and 180 mK for the integral Joule-Thomson effect. The direct measurement results are given for pure methane in the temperature range between room temperature and about 580 K at pressures up to 7 MPa, and for {xC(2)H(6) + (1-x)CH4} at x=0.11 and x=0.25 for p=7MPa in the temperature range between 380 K and 480 K. Other properties such as enthalpy residual and molar heat capacity at constant pressure are also derived and correlated. Good agreement was found with available experimental results from the literature and with the prediction made by the accurate Wagner-Setzmann equation of state for methane. Our results confirm the validity of our experimental and evaluation procedures and extend the experimentally investigated temperature range for methane. Further results for binary and ternary mixtures with water will be published in a subsequent paper.