a rigid tank of volume 0.26 m^3 contains hydrogen at 15 C and101 KPa. A paddlewh

Question

a rigid tank of volume 0.26 m^3 contains hydrogen at 15 C and101 KPa. A paddlewheel stirs the tank, adding 17.8 kJ of work. Overthe same time period, the tank loses 9.3 kJ of heat to theenvironment. Assuming the specific heat of hydrogen does not varywith temperature, find the final temperature LifeSaver!!! a rigid tank of volume 0.26 m^3 contains hydrogen at 15 C and101 KPa. A paddlewheel stirs the tank, adding 17.8 kJ of work. Overthe same time period, the tank loses 9.3 kJ of heat to theenvironment. Assuming the specific heat of hydrogen does not varywith temperature, find the final temperature LifeSaver!!!

Explanation / Answer

given for hydrogen, P = 101 kPa, V = 0.26 m3, T = 15 C =288.15 K using ideal gas equation, nR = PV/T = 101*1000*0.26/288.15 =91.13 J/K heat capacity at const volume Cv is given by nR/(-1) hydrogen is a diatomic gas for which = 1.4 thus, Cv = 91.13/(1.4-1) = 227.82 J/K from 1st law of thermodynamics, Q =U+W here Q = -9.3 kJ, W = -17.8 kJ so, U = -9.3+17.8 = 8.5 kJ or, CvdT = 8.5 kJ or, dT = (8.5*1000 J)/(227.82J) = 37.31 K Thus final temperature = 15 + 37.31 = 52.31C {note that T in Kelvin and Celcius are same}

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