Question

A complex mixture such as ice cream is stored in a rigid vessel to cool before further processing. The 5000 kg mixture loses 7.5 kW heat over 4 hours.

(a)

Find the change in internal energy of the fluid (kJ).

(b)

The vessel is upgraded to handle a larger capacity. The mass of the mixture is doubled. Will the change in internal energy of the ice cream increase, decrease, or stay the same?

Answer 1

The vessel is rigid i.e there is no expansion of the vessel.

Considering the vessel as the system,

By first law of thermodynamics, we get

dU= Q+W.... 1.

a) Where heat is taken out from the system So Q= -7.5 kW

There is no work done on the system, Hence W= 0

From 1.

dU= Q

dU= -7.5 kW

But we want it in kJ.

So time required is 4 hrs for the process.

Hence,

dU= -7.5 (kJ/sec)×4×60(sec)

dU= -1800 kJ

b) In this case mass of the mixture is doubled i.e m= 10000 kg

dU= Q

As Q is a intensive property,

Hence dU has also became an intensive property which is independent of mass.

Hence dU value remains the same as -1800 kJ.