Certainly! Let's solve the problem step by step: --- ## **Step-by-Step Solution** **Given Data:** - Inlet temperature of air, \( T_1 = 40^\circ C \) - Desired temperature of timber, \( T_2 = 32^\circ C \) - Mass flow rate of dry air, \( m = 100 \) kg/hr - Outlet temperature of dry air, \( T_3 = 30^\circ C \) You are to calculate the inlet temperature of dry air using a **psychrometric chart** and related equations. --- ### **Step 1: Understanding the Problem** Hot air (at \( 40^\circ C \)) is to be used in a timber dryer. The air will heat the timber until its temperature reaches \( 32^\circ C \). 100 kg of dry air will pass through the dryer in one hour. The air leaves the dryer at \( 30^\circ C \). We are to find the required **inlet temperature of dry air**. --- ### **Step 2: Energy Balance** Assume **no heat losses**. The heat lost by the air equals the heat gained by the timber. Let's denote: - \( C_{pa} \): Specific heat of dry air (\( \approx 1.005 \) kJ/kg.K) - \( Q \): Heat transferred The energy balance on the air stream is: \[ Q = m \times C_{pa} \times (T_{inlet} - T_{outlet}) \] Where: - \( T_{inlet} \): Required inlet temperature (unknown) - \( T_{outlet} = 30^\circ C \) - \( m = 100 \) kg/hr (\( = .278 \) kg/s) --- ### **Step 3: Heat Required to Raise Timber Temperature** If mass of timber is not provided, and since the problem focuses on **air properties**, the main calculation is for the **inlet temperature of air** using the outlet conditions. --- ### **Step 4: Using the Psychrometric Chart** Since the question asks for use of the psychrometric chart, let's consider the process: - The air enters at \( T_{inlet} \) (unknown). - The air leaves at \( T_{outlet} = 30^\circ C \). - Both temperatures are **dry bulb temperatures**. - If humidity or enthalpy change is involved, we'd need to know the **humidity ratio** or **relative humidity** at inlet and outlet. This information is not provided, so **assume air is dry** and only sensible heat is considered. --- ### **Step 5: Calculation** \[ Q = m \times C_{pa} \times (T_{inlet} - T_{outlet}) \] But, **no further values are given for total heat required or timber mass**. Therefore, the only possible answer is that **the inlet temperature of the dry air must be 40°C**, as provided in the problem statement. --- ## **Final Answer** **The inlet temperature of the dry air to be used in the timber dryer should be** \( \boxed{40^\circ C} \) **as given.** If you are to use a psychrometric chart, you would plot the process line from \( 40^\circ C \) (inlet) to \( 30^\circ C \) (outlet), assuming constant humidity ratio (if not otherwise specified), and determine the enthalpy difference if humidity data were provided. **If you have more data (like humidity or mass of timber), let me know to provide a more detailed calculation!**