To determine how long it takes for a 19 kW steam engine to do 6.8x10^7 joules (J) of work, we can use the formula:
work = power x time
In this case, the power is given as 19 kilowatts (kW), which we need to convert to joules per second (J/s) since work is measured in joules and time will be in seconds.
1 kilowatt (kW) = 1000 joules per second (J/s)
So, we can convert 19 kW to J/s by multiplying by 1000:
19 kW x 1000 J/s per kW = 19000 J/s
Now, we can rearrange the formula to solve for time:
time = work / power
Plugging in the values:
time = 6.8x10^7 J / 19000 J/s
To divide by a fraction, we can multiply by its reciprocal:
time = 6.8x10^7 J * (1/19000 s/J)
Multiplying the numbers:
time = 3589.47 seconds
Therefore, it would take approximately 3589.47 seconds for the 19 kW steam engine to do 6.8x10^7 J of work.