Math behind heating a carom table.

nataddrho

www.digicue.net
Silver Member
I was seeing a lot of conflicting information online so I did the math myself:

Slate is 1.555 oz/in3. The slate mass of 10-foot carom table with 1.2 inch thick slate is approximately 1.555 x 1.2 x 10 x 5 x 12^2 / 16 = 840 lbs (381 kg). That is about 280 lbs per slate piece considering 3 pieces.

The specific heat capacity of slate is 0.76 kJ/(kg*K). To heat the entire slate 5 degrees C above ambient temperature, it would take 0.76 x 381 x 5 = 1448 kJ of energy.

Assuming a carom table heater can output 500W, and maybe only 75% efficient at heating the table (because of losses due to power conversion and heating the air under the table), then the time it would take to soak this energy into the slate is 1448 kJ / (0.75 * 0.5kW * 3600 seconds/hr) = 1.0 hours.

After ambient+5C is reached, lets further assume that the duty cycle of the heater drops to 50% to maintain temperature. So every additional hour after the first will consume 250W.

A final assumption is that the water in the cloth will take a full 1 hour at +5C to evaporate.

A kWh currently costs about $0.25. So if I turn on a carom table heater 2 hours in advance of playing, it will only cost $0.25 * (0.5kWh + 0.25kWh) = $0.19.

Alternatively, if I keep my carom table heater on all of the time, then (ignoring humidity fluctuations throughout the day), approximately $0.25 * 0.25kW * 24 * 30 = $45 per month.
 
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