Thermodynamics

1. Correct Answer: 32.29 ± 4%

A 1.4 m3 tank fills through inlet A while supplying waterthrough outlets B and C at the rates given below. Determine howlong (minutes) it will take until the tank is full if initially thetank contains 277 kg of water. The flow rates are given in kg/minwhere \"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 atemperature of 507.6 K. Determine the power (kW) for the compressorif the inlet volumetric flow rate is 0.244 m3 /s and the heattransfer through the shell of the compressor to the surroundings is1.35 kW. Use the ideal gas tables (variable specific heats).

3.

(ans:19.6)

A well-insulated, full, water tank containing 198 kg of waterinitially at 44^oC is being supplied with15.6^oC water at a rate of 4 kg/min. Water is exiting thetank at the same flow rate so that the mass of water in the tankremains constant. Circulation in the tank keeps the water at auniform temperature. The specific heat of the water is given as C =4.2 kJ/kg-K. Determine the time (minutes) at which the watertemperature 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 k1and k2