Question

Thermodynamics

1. Correct Answer: 32.29 ± 4%

A 1.4 m3 tank fills through inlet A while supplying water through outlets B and C at the rates given below. Determine how long (minutes) it will take until the tank is full if initially the tank contains 277 kg of water. The flow rates are given in kg/min where "t" is in minutes.

All flows are at 20 C.

Mass flow rate of A = 3.5 + 2.1*t

Mass flow rate of B = 1.5

Mass flow rate of C = 1.2

2.

Correct Answer: -99.69 ± 1%

Air enters a compressor at 152 kPa and 290 K and exits at a temperature of 507.6 K. Determine the power (kW) for the compressor if the inlet volumetric flow rate is 0.244 m3 /s and the heat transfer through the shell of the compressor to the surroundings is 1.35 kW. Use the ideal gas tables (variable specific heats).

3.

(ans:19.6)

A well-insulated, full, water tank containing 198 kg of water initially at 44^oC is being supplied with 15.6^oC water at a rate of 4 kg/min. Water is exiting the tank at the same flow rate so that the mass of water in the tank remains constant. Circulation in the tank keeps the water at a uniform temperature. The specific heat of the water is given as C = 4.2 kJ/kg-K. Determine the time (minutes) at which the water temperature drops to 34.7^oC.

Note: The energy of water in the tank is given as: E = m_cv*C*T

The solution for an equation of the form: a*dT/dt + T +b = 0     is

T(t) = k1*exp(-t/a) + k2

For this problem, the given constraints are:

T(t=0) = T_initial

T(t=infinity) = T_inlet

Hint: Use the given constraints to determine the constants k1 and k2

Answer 1