Q$.$ A $30,000$ m$3$ tank contains pressurized water.

a$)$ Determine the change in internal energy of water when its temperature increased from $10$

$\backslash$deg C to $160\backslash$deg C$.$ This is actually the energy stored in this tank by changing the temperature

$($and hence internal energy of water$).$ We will assume there is no unwanted energy loss.

Means of this temperature change are not given. That will be another problem later. For

simplicity assume i$)$ the water always remains in a liquid state $($this requires pressure

above $6\mathrm{.}2$ bar for water$)$; ii$)$ the specific heat of the water is constant at c$=4180$ J$/($kg K$)$;

b$)$ How much energy would be stored if the same volume were filled with Helium, and it

experienced the same temperature change? For simplicity assume i$)$ constant volume

specific heat of Helium is cv$=810$ J$/($kg K$)$ and it is constant; ii$)$ you decide what should

be the pressure of the Helium in the tank which will also determine the mass of the

helium in the tank.

c$)$ Comparing your results of parts a$)$ and b$)$ above what can you tell about capacity of such

energy storage systems. Is one option better than the other? Are there any potential issues

with either of the options?