African solar systems part 8: heat storage and steam

Classical Mechanics Level 5

Introduction

There are multiple energy demands on the CSP. For a small village one might have daily heat needed for sterilizing water, cooking, and electricity, in particular :

Electricity to charge 100 cellular phones or radios daily.
Electricity to charge 200 10 W LED lamps for 3 hours of use daily.
Heat to sterilize 3000 L of water daily.
Heat to cook 1000 meals daily. Heat must be provided to cook 10 percent of meals up to three hours after sunset.
Continuous (24 hour) operation of a low power cellular base station (for example a Vanu base station at 100 W).

If you look at the energy requirements above, you will notice that typically lamps and cooking require heat storage, as those may happen when the sun goes down. Heat storage is a major benefit for CSP systems vs. photo-voltaic systems as a solar panel can't store any heat. One cannot hold much heat with steam, however, as it's not very practical for the amount of heat needed for everyday life.

The question

To see the difficulty with steam, consider the requirement that 100 meals need to be able to be cooked three hours after sunset. We will model the amount of heat used to cook a meal as the heat necessary to take a 100 g strip of meat (specific heat of most meats is around 3 kJ/(kg K)) from 25 $^\circ$ C to the safe temperature of 75 $^\circ$ C. Therefore, at a minimum, we will need to have enough heat to do this 100 times, 3 hours after sunset.

We wish to hold the necessary heat to cook with as 250 $^\circ$ C steam inside a perfectly insulated tank of volume 2 $m^3$ . What pressure must the steam then be held at in Pascals ?

Assume that you can extract all the heat from the steam until it reaches 100 $^\circ$ C. We want to keep the steam as steam, so we will not extract any further heat, which would make the steam condense. Take the molar specific heat of steam to be 36 J/(mol K).

As you will see from the question above, the steam must have a pressure greater than atmospheric pressure. Pressurized superhot steam is stressful on material components and dangerous in a residential area. A better way of storing heat is to use a special substance. Molten salt is the current technology of choice for heat storage. A common mixture is 60 percent sodium nitrate ( $NaNO_3$ ), 40 percent potassium nitrate ( $KNO_3$ ). Both of these compounds are used in fertilizers and hence they are both nontoxic and cheap. This is a eutectic mixture, which means the concentrations are in the right proportion to minimize the temperature at which the salt becomes a solid. Despite being eutectic, this mixture still melts at 221 $^\circ$ C (and freezes at 238 $^\circ$ C). The specific heat of the salt at around 1550 $J/kg~K$ is lower than that of water (4186 $J/kg~K$ ), but since the salt doesn't vaporize one can store large amounts of heat while maintaining low pressures.

The answer is 604000.

1 solution

Beakal Tiliksew
Apr 13, 2014

$\\ \Delta { T }_{ 1 }={ 75 }^{ \circ }-{ 25 }^{ \circ }\\ \\ \Delta { T }_{ 2 }={ 250 }^{ \circ }-{ 100 }^{ \circ }\\ \\ T={ 250 }^{ \circ }\\$

Where

$Q=100(m{ C }_{ s }\Delta { T }_{ 1 })\quad ....\quad \quad \quad \quad (1)\\ \\ Q=n{ C }_{ v }\Delta { T }_{ 2 }\quad \quad \quad \quad .....\quad \quad \quad \quad \quad (2)\\ \\ PV=nRT\quad \quad \quad \quad \quad \quad \quad ......\quad \quad \quad (3)\quad \quad \quad \quad \quad \quad \quad \\$

Re-arrange for $P$ , and substitute all the known values you get

$P\approx 604000$

African solar systems part 8: heat storage and steam

The answer is 604000.

1 solution

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