To calculate the amount of heat energy (Q) required to raise the temperature of the water from 5.0°C to 42°C, we can use the formula:
Q = mcΔT
Where Q is the heat energy in joules (J), m is the mass of water in grams (g), c is the specific heat capacity of water (4.184 J/g°C), and ΔT is the change in temperature in degrees Celsius (°C).
So, plugging in the values given in the problem:
m = 250.0 g
ΔT = (42°C - 5.0°C) = 37°C
c = 4.184 J/g°C
Q = (250.0 g) x (4.184 J/g°C) x (37°C)
Q = 39,050 J
Therefore, the amount of heat energy (Q) required to raise the temperature of 250.0 g of water from 5.0°C to 42°C is 39,050 J.
To convert the answer into calories (cal), we can use the conversion factor that 1 cal = 4.184 J.
So, the amount of heat energy (Q) required in calories is:
Q = (39,050 J) / (4.184 J/cal)
Q = 9,334 cal (rounded to 4 significant figures)
Therefore, the amount of heat energy (Q) required to raise the temperature of 250.0 g of water from 5.0°C to 42°C is 39,050 J or 9,334 cal.