5 kg of a gas with a molecular weight of 32 kg/kmol and a temperature of 110 C i

Question

5 kg of a gas with a molecular weight of 32 kg/kmol and a temperature of 110 C is contained in a closed rigid tank fitted with an electric resistor whose mass is negligible. The resistor draws a constant current of 12 amps at a voltage of 125 V for 5 minutes. Measurements indicate that when equilibrium is reached, the temperature of the gas has increased by 44.1 C. Heat transfer from the is estimated to occur at a constant rate of 1kw. Assuming ideal gas behavior and negligible kinetic and potential effects, determine an average value of the specified heat, C_p, in kj/kg*K, of the gas in this temperature interval based on the measured data.

Explanation / Answer

Heat transfer rate from the gas =Houtput =  1kW

Electric resistor emits heat at a rate =VI = 12*125 W = Hinput = 1.5kW

Rate of change of enthalpy of the gas = Heat input - heat output = 0.5kW

Let cp be the specific heat, the total change in enthalpy = mcp T

which is eqaul to  0.5kW times the total time (5min = 300s)

T is given 44.1K

mcp T = 0.5kW*300s

5kg * cp *44.1K = 150kJ

cp =150kJ /(5kg *44.1K ) = 0.68 kJ kg-1K-1

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