A Cherenkov detector which ignores the directionality of the radiation and solely integrates all photons having energies above the threshold energy is known as a threshold Cherenkov detector. Since, the minimum particle energy required to produce Cherenkov radiation is a function of the refractive index of the radiating material; the threshold particle energy can be varied if the radiating material is a gas. A gas threshold Cherenkov detector thus offers a direct and convenient means of measuring the integral intensity of cosmic ray muons at different energies by varying the pressure in the chamber. To determine the shape of a portion of the cosmic ray muon energy distribution, a threshold Cherenkov detector sensitive to muons with energies between around 1 to 5 GeV is constructed. Currently, the tube is operated in the range of 2 to 16 atm pressure and the preliminary results from the experimental findings are reported. In future, these measurements shall be compared to the predictions from the CORSIKA simulation package. Through this, the feasibility of using a threshold Cherenkov detector is inferred to accurately measure the shape of the cosmic ray muon energy distribution in the mentioned energy range.