Answer:
Approximately 3318 disintegrations per minute.
Explanation:
The activity 
of a radioactive decay at time 
can be found with the following equation:
.
In this equation,
is the natural base. 
.
is the initial activity of the decay. For this question, 
.- The decay constant
of this sample needs to be found.
The decay constant here can be found using the activity after 10 days. As long as both times are in the same unit (days in this case,) conversion will not be necessary.
.
.
Apply the natural logarithm to both sides of this equation.
.
.
.
Note that the unit of the decay constant is 
(the reciprocal of days.) The exponent 
should be dimensionless. In other words, the unit of should also be days. This observation confirms that there's no need for unit conversion as long as the two times are in the same unit.
Apply the equation for decay activity at time to find the decay activity after 47.2 days.
.
By dimensional analysis, the unit of activity here should also be disintegrations per minute. The activity after 47.2 days will be approximately 3318 disintegrations per minute.
H2SO4 + 2KOH ---> K2SO4 + 2H2O
:)
The initial temperature is 137.34 °C.
<u>Explanation:</u>
As the specific heat formula says that the heat energy required is directly proportional to the mass and change in temperature of the system.
Q = mcΔT
So, here the mass m is given as 23 kg, the specific heat of steel is given as c = 490 J/kg°C and the initial temperature is required to find with the final temperature being 140 °C. Also the heat energy required is 30,000 J.
ΔT =
ΔT =
Since the difference in temperature is 2.66, then the initial temperature will be
Final temperature - Initial temperature = Change in temperature
140-Initial temperature = 2.66
Initial temperature = 140-2.66 = 137.34 °C
Thus, the initial temperature is 137.34 °C.
