2. A container initially holds 7 kg of liquid water at 325K. Liquid water starts

Question

2. A container initially holds 7 kg of liquid water at 325K. Liquid water starts to flow into the container at an accelerated rate of 0.1*t (kg/s2) at 350K. Water is withdrawn from the container with a constant rate of 0.2 kg/s. The container is cooled from the outside to maintain a constant temperature of 325K. The cooling sink can withdraw variable heat rates up to 4000 k]/s. Assume that the pressure is constant and uniform in the system and surroundings. Assume complete and immediate mixing inside the system and that for water, C Cy Cp 4200 J/kgK. After how much time will the flow of liquid water exceed the cooling capacity of the refrigeration element and the temperature will start to change in the container? How much water is inside the container at the moment the temperature begins to change? d(mU) a. b. Hints: but can be written asmd where one of the terms IS - 0. For this process, U H- CvT....think about why For part (b), write an equation for the mass in the control volume at time t and plug in the time you got in part (a)

Explanation / Answer

at ant time mass coming rate to container = m

now (dm/dt) = 0.1 t or m= 0.1t2 kg/s at temperature of 350 K

mass going out at any time = 0.2 kg/s at temperature of 325 K

Now heat coming rate = mCpT = 0.1t2*4200*350

heat going out rate = mout*CpTout = 0.2*4200*325

at breakeven point (when flow exceeds cooling capacity);

heat coming -heat going = cooling capacity

0.1t2*4200*350-0.2*4200*325 = 4000*1000 this gives t2 = 1884.36 or t = 43.4 sec

You have asked only for solution of a part. Please note a hint for solution of b part is that you will have to calulate the total mass came in 43.4 sec (by using the mass rate equation derived in option a) and total mass went out in 43.4 sec

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