To calculate the heat input required to heat chlorine gas from 120°C to 180°C at constant pressure, the specific heat capacity of chlorine gas is needed. The heat input is calculated by using the formula Q = n × Cp × ΔT, where n is the flow rate in moles per hour, Cp is specific heat capacity, and ΔT is the temperature change. The result is then converted from kJ/hr to kW to get the heat input in the desired units.
To calculate the heat input required to heat chlorine gas from 120°C to 180°C at constant pressure for a flow rate of 15.0 kmol/min, follow these steps:
Molar Mass of Chlorine (Cl2): Chlorine's molar mass (Cl2) is approximately 70.9 g/mol.
Conversion to Mass Flow Rate: Convert the given flow rate from kilomoles to moles per minute : 15.0kmol/min=15.0×10³mol/min
Heat Capacity Calculation: The heat capacity at constant pressure (Cₚ)for chlorine gas is approximately 0.478 kJ/(kg·°C) at room temperature.
Mass Calculation: Calculate the mass of chlorine gas flowing per minute:15.0×10³mol/min×70.9g/mol=mass in grams.
Energy Required for Temperature Increase: Use the formula Q=mCₚ ΔT to find the heat input, where Q is heat input, m is mass,Cₚ is specific heat capacity, and ΔT is the temperature change.
Temperature Change Calculation: ΔT=180°C−120°C=60°C.
Conversion of ΔT to Kelvin: 60°C=60+273.15K=333.15K.
Calculation of Heat Input:Q=(mass in kg)×Cₚ ×ΔT. to find the heat input in kJ.
Conversion to kW: Convert the obtained heat input from kJ to kW(1 kW = 1 kJ/s).
Perform the calculations using the given values to find the heat input in kW for the given conditions.
Complete Question:
WP Chlorine gas is to be heated from 120°C and 1 atm to 180°C. Calculate the heat input (kW) required to heat a stream of the gas flowing at 15.0 kmol/min at constant pressure.