During a winter day, the external temperature is 0^ C with a relative humidity of 40 % . This outside air enters a room where it is heated to 20^ C . Determine the relative humidity inside the room. The saturation vapour pressure is 4.6 mm of mercury at 0^ C and 18 mm of mercury at 20^ C .

Step-by-step solution

The relative humidity (RH) is defined as the ratio of the actual vapour pressure to the saturation vapour pressure at a given temperature. Given: External temperature, T₁ = 0^ C Relative humidity at 0^ C , RH ₁ = 40 % Saturation vapour pressure at 0^ C , P_ s1 = 4.6 mm of Hg The actual vapour pressure of the outside air at 0^ C is: P_ v1 = RH ₁ 100 P_ s1 = 40 100 4.6 = 1.84 mm of Hg When the outside air enters the room and is heated to 20^ C , the process occurs at a constant atmospheric pressure. Since the mole fr