Question

Water enters a storage tank at a temperature, \( T_0 \) and flow rate, \( Q_0 \) and leaving at a flow rate, \( Q \) and temperature, \( T \). There are negligible heat losses in the tank. The area of cross-section of the tank is \( A_c \). The model equation that describes the water temperature variation in the tank is given by:

• A. \( Q(T_0 - T) = A_c h \frac{dT}{dt} \)
• B. \( Q T_0 - Q T = A_c h \frac{dT}{dt} \)
• C. \( Q(T_0 - T) = A_c h \frac{dT}{dt} \)
• D. \( Q(T_0 - T) = A_c h \frac{d(T_h)}{dt} \)

Hint:

The temperature change of a fluid in a tank depends on the flow rates and the heat transfer properties, as given by the energy balance.

Answer 1

The Correct Option is A

Step 1: Recall the energy balance equation for the tank.
The rate of change of temperature inside the tank depends on the inflow rate, outflow rate, and the heat transfer. The correct model for this situation is given by the equation in option (A).

Step 2: Conclusion.
The correct answer is (A).