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From this NASA pdf:

At 46:40:02 Mission Elapsed Time during the Apollo 13 mission, both oxygen tank fans were powered on, hopefully to get a more accurate reading of the tank pressure.

In fact, the pressure is not influenced by fan operation. The reading of the capacitance tank gauge depends on a constant temperature of tank contents.

56 hours into the mission, at about 03:06 UT on 14 April 1970 (10:06 PM, April 13 EST), the power fans were turned on within the tank for the third "cryo-stir" of the mission, a procedure to stir the oxygen slush inside the tank which would tend to stratify. The exposed fan wires shorted and the teflon insulation caught fire in the pure oxygen environment. This fire rapidly heated and increased the pressure of the oxygen inside the tank, and may have spread along the wires to the electrical conduit in the side of the tank, which weakened and ruptured under the pressure, causing the no. 2 oxygen tank to explode. This damaged the no. 1 tank and parts of the interior of the service module and blew off the bay no. 4 cover.

Image and quote from this NASA page.

Through the first 46 hours of the mission, telemetered data and crew observations indicated that the performance of oxygen tank 2 was normal. At 046:40:02, the crew routinely turned on the fans in oxygen tank 2. Within three seconds, the oxygen tank 2 quantity indication changed from a normal reading of about 82 percent full to an obviously incorrect “off-scale high” reading of over 100 percent. Analysis of the electrical wiring of the quantity gauge revealed that this erroneous reading could have been caused by either a short circuit or an open circuit in the gauge wiring or a short circuit between the gauge plates. Subsequent events indicated that a short was the more likely failure mode.

At 047:54:50 and at 051:07:44, the oxygen tank 2 fans were turned on again, with no apparent adverse effects. The quantity gauge continued to read off-scale high.

From this NASA page.

So the fans were activated to mix the supercritical fluid oxygen to get a uniform temperature and uniform density for a better result from the capacitive filling level probe. Previous readings were above 100 %.

As Organic Marble mentioned, the tank stored neither gaseous nor liquid nor solid oxygen. The oxygen was in another state, the supercritical fluid.

From this NASA pdf:

At 46:40:02 Mission Elapsed Time during the Apollo 13 mission, both oxygen tank fans were powered on, hopefully to get a more accurate reading of the tank pressure.

In fact, the pressure is not influenced by fan operation. The reading of the capacitance tank gauge depends on a uniform temperature of tank contents.

56 hours into the mission, at about 03:06 UT on 14 April 1970 (10:06 PM, April 13 EST), the power fans were turned on within the tank for the third "cryo-stir" of the mission, a procedure to stir the oxygen slush inside the tank which would tend to stratify. The exposed fan wires shorted and the teflon insulation caught fire in the pure oxygen environment. This fire rapidly heated and increased the pressure of the oxygen inside the tank, and may have spread along the wires to the electrical conduit in the side of the tank, which weakened and ruptured under the pressure, causing the no. 2 oxygen tank to explode. This damaged the no. 1 tank and parts of the interior of the service module and blew off the bay no. 4 cover.

Image and quote from this NASA page.

Through the first 46 hours of the mission, telemetered data and crew observations indicated that the performance of oxygen tank 2 was normal. At 046:40:02, the crew routinely turned on the fans in oxygen tank 2. Within three seconds, the oxygen tank 2 quantity indication changed from a normal reading of about 82 percent full to an obviously incorrect “off-scale high” reading of over 100 percent. Analysis of the electrical wiring of the quantity gauge revealed that this erroneous reading could have been caused by either a short circuit or an open circuit in the gauge wiring or a short circuit between the gauge plates. Subsequent events indicated that a short was the more likely failure mode.

At 047:54:50 and at 051:07:44, the oxygen tank 2 fans were turned on again, with no apparent adverse effects. The quantity gauge continued to read off-scale high.

From this NASA page.

So the fans were activated to mix the supercritical fluid oxygen to get a uniform temperature and uniform density for a better result from the capacitive filling level probe. Previous readings were above 100 %.

As Organic Marble mentioned, the tank stored neither gaseous nor liquid nor solid oxygen. The oxygen was in another state, the supercritical fluid.

From this NASA pdf:

At 46:40:02 Mission Elapsed Time during the Apollo 13 mission, both oxygen tank fans were powered on, hopefully to get a more accurate reading of the tank pressure.

56 hours into the mission, at about 03:06 UT on 14 April 1970 (10:06 PM, April 13 EST), the power fans were turned on within the tank for the third "cryo-stir" of the mission, a procedure to stir the oxygen slush inside the tank which would tend to stratify. The exposed fan wires shorted and the teflon insulation caught fire in the pure oxygen environment. This fire rapidly heated and increased the pressure of the oxygen inside the tank, and may have spread along the wires to the electrical conduit in the side of the tank, which weakened and ruptured under the pressure, causing the no. 2 oxygen tank to explode. This damaged the no. 1 tank and parts of the interior of the service module and blew off the bay no. 4 cover.

Image and quote from this NASA page.

Through the first 46 hours of the mission, telemetered data and crew observations indicated that the performance of oxygen tank 2 was normal. At 046:40:02, the crew routinely turned on the fans in oxygen tank 2. Within three seconds, the oxygen tank 2 quantity indication changed from a normal reading of about 82 percent full to an obviously incorrect “off-scale high” reading of over 100 percent. Analysis of the electrical wiring of the quantity gauge revealed that this erroneous reading could have been caused by either a short circuit or an open circuit in the gauge wiring or a short circuit between the gauge plates. Subsequent events indicated that a short was the more likely failure mode.

At 047:54:50 and at 051:07:44, the oxygen tank 2 fans were turned on again, with no apparent adverse effects. The quantity gauge continued to read off-scale high.

From this NASA page.

So the fans were activated to mix the supercritical fluid oxygen to get a uniform temperature and uniform density for a better result from the capacitive filling level probe. Previous readings were above 100 %.

As Organic Marble mentioned, the tank stored neither gaseous nor liquid nor solid oxygen. The oxygen was in another state, the supercritical fluid.

From this NASA pdf:

At 46:40:02 Mission Elapsed Time during the Apollo 13 mission, both oxygen tank fans were powered on, hopefully to get a more accurate reading of the tank pressure.

In fact, the pressure is not influenced by fan operation. The reading of the capacitance tank gauge depends on a constant temperature of tank contents.

56 hours into the mission, at about 03:06 UT on 14 April 1970 (10:06 PM, April 13 EST), the power fans were turned on within the tank for the third "cryo-stir" of the mission, a procedure to stir the oxygen slush inside the tank which would tend to stratify. The exposed fan wires shorted and the teflon insulation caught fire in the pure oxygen environment. This fire rapidly heated and increased the pressure of the oxygen inside the tank, and may have spread along the wires to the electrical conduit in the side of the tank, which weakened and ruptured under the pressure, causing the no. 2 oxygen tank to explode. This damaged the no. 1 tank and parts of the interior of the service module and blew off the bay no. 4 cover.

Image and quote from this NASA page.

Through the first 46 hours of the mission, telemetered data and crew observations indicated that the performance of oxygen tank 2 was normal. At 046:40:02, the crew routinely turned on the fans in oxygen tank 2. Within three seconds, the oxygen tank 2 quantity indication changed from a normal reading of about 82 percent full to an obviously incorrect “off-scale high” reading of over 100 percent. Analysis of the electrical wiring of the quantity gauge revealed that this erroneous reading could have been caused by either a short circuit or an open circuit in the gauge wiring or a short circuit between the gauge plates. Subsequent events indicated that a short was the more likely failure mode.

At 047:54:50 and at 051:07:44, the oxygen tank 2 fans were turned on again, with no apparent adverse effects. The quantity gauge continued to read off-scale high.

From this NASA page.

So the fans were activated to mix the supercritical fluid oxygen to get a uniform temperature and uniform density for a better result from the capacitive filling level probe. Previous readings were above 100 %.

As Organic Marble mentioned, the tank stored neither gaseous nor liquid nor solid oxygen. The oxygen was in another state, the supercritical fluid.

From this NASA pdf:

At 46:40:02 Mission Elapsed Time during the Apollo 13 mission, both oxygen tank fans were powered on, hopefully to get a more accurate reading of the tank pressure.

56 hours into the mission, at about 03:06 UT on 14 April 1970 (10:06 PM, April 13 EST), the power fans were turned on within the tank for the third "cryo-stir" of the mission, a procedure to stir the oxygen slush inside the tank which would tend to stratify. The exposed fan wires shorted and the teflon insulation caught fire in the pure oxygen environment. This fire rapidly heated and increased the pressure of the oxygen inside the tank, and may have spread along the wires to the electrical conduit in the side of the tank, which weakened and ruptured under the pressure, causing the no. 2 oxygen tank to explode. This damaged the no. 1 tank and parts of the interior of the service module and blew off the bay no. 4 cover.

Image and quote from this NASA page.

Through the first 46 hours of the mission, telemetered data and crew observations indicated that the performance of oxygen tank 2 was normal. At 046:40:02, the crew routinely turned on the fans in oxygen tank 2. Within three seconds, the oxygen tank 2 quantity indication changed from a normal reading of about 82 percent full to an obviously incorrect “off-scale high” reading of over 100 percent. Analysis of the electrical wiring of the quantity gauge revealed that this erroneous reading could have been caused by either a short circuit or an open circuit in the gauge wiring or a short circuit between the gauge plates. Subsequent events indicated that a short was the more likely failure mode.

At 047:54:50 and at 051:07:44, the oxygen tank 2 fans were turned on again, with no apparent adverse effects. The quantity gauge continued to read off-scale high.

From this NASA page.

So the fans were activated to mix the supercritical fluid oxygen to get a uniform temperature and uniform density for a better result from the capacitive filling level probe. Previous readings were above 100 %.

As Organic Marble mentioned, the tank stored neither gaseous nor liquid oxygen. The oxygen was in another state, the supercritical fluid.

From this NASA pdf:

At 46:40:02 Mission Elapsed Time during the Apollo 13 mission, both oxygen tank fans were powered on, hopefully to get a more accurate reading of the tank pressure.

56 hours into the mission, at about 03:06 UT on 14 April 1970 (10:06 PM, April 13 EST), the power fans were turned on within the tank for the third "cryo-stir" of the mission, a procedure to stir the oxygen slush inside the tank which would tend to stratify. The exposed fan wires shorted and the teflon insulation caught fire in the pure oxygen environment. This fire rapidly heated and increased the pressure of the oxygen inside the tank, and may have spread along the wires to the electrical conduit in the side of the tank, which weakened and ruptured under the pressure, causing the no. 2 oxygen tank to explode. This damaged the no. 1 tank and parts of the interior of the service module and blew off the bay no. 4 cover.

Image and quote from this NASA page.

Through the first 46 hours of the mission, telemetered data and crew observations indicated that the performance of oxygen tank 2 was normal. At 046:40:02, the crew routinely turned on the fans in oxygen tank 2. Within three seconds, the oxygen tank 2 quantity indication changed from a normal reading of about 82 percent full to an obviously incorrect “off-scale high” reading of over 100 percent. Analysis of the electrical wiring of the quantity gauge revealed that this erroneous reading could have been caused by either a short circuit or an open circuit in the gauge wiring or a short circuit between the gauge plates. Subsequent events indicated that a short was the more likely failure mode.

At 047:54:50 and at 051:07:44, the oxygen tank 2 fans were turned on again, with no apparent adverse effects. The quantity gauge continued to read off-scale high.

From this NASA page.

So the fans were activated to mix the supercritical fluid oxygen to get a uniform temperature and uniform density for a better result from the capacitive filling level probe. Previous readings were above 100 %.

As Organic Marble mentioned, the tank stored neither gaseous nor liquid nor solid oxygen. The oxygen was in another state, the supercritical fluid.