Show all your steps and draw diagrams where necessary. Add explanatory notes whe
ID: 249420 • Letter: S
Question
Show all your steps and draw diagrams where necessary. Add explanatory notes where necessary.
1. A child complains that her milk is too hot. It is indeed too hot at 90o C. Her mother pours 80 g of cold milk at 7oC to the 160 g milk already in the cup. If the specific heart capacity of milk is 3800 J.kg-1.K-1, what is the temperature of the mixture now?
2. During a nuclear reactor accident, 500 m3 of water at 20o C is pumped into the reactor core which is producing heat at the rate of 250 MW. If the water is allowed to boil at normal atmospheric pressure how long will it take to boil away all this water?
3. 600 J of work is done to compress a given mass of gas isothermally to half its initial volume. How much work is required to compress the same amount of gas isothermally to 20th of its original volume?
Explanation / Answer
1)
t1 = 90 C
t_milk = 7 C
t2 = ?
m_cold = 0.08 kg
m_hot 0.16 kg
shc = 3800 J.kg^-1.K^-1
T = (m1T1+m2T2)/(m1+m2) = (80*7+160*90)/240 = 62.333 C.
2)
During a nuclear reactor accident, 500 m3 of water at 20o C is pumped into the reactor core which is producing heat at the rate of 250 MW. If the water is allowed to boil at normal atmospheric pressure how long will it take to boil away all this water?
Specific heat of water = 4186 Joules / (kg * °C)
the heat of vaporization of water = 2.26 * 10^6 Joules/ kg
1 m^3 of water = 1000 kg
500 m^3 of water = 500,000 kg = 5 * 10^5 kg
Heat energy required to increase temperature of water from 20°C to 100°C = mass * Specific heat * Temperature
Temperature = 100 – 20 = 80°C
Heat energy = 5 * 10^5 * 4186 * 80 = 1.6744 * 10^11 Joules
Heat energy required to boil water at normal atmospheric pressure = heat of vaporization * mass
Heat energy = 2.26 * 10^6 Joules/ kg * 5 * 10^5 kg
Heat energy = 1.13 * 10^12 Joules
The total heat energy = 1.6744 * 10^11 + 1.13 * 10^12 = 1.29744 * 10^12 Joules
Power = energy ÷ time
Energy = Power * time
the reactor core which is producing heat at the rate of 250 MW
250 MW = 250 mega-watt = 250 million watts = 2.50 * 10^8 watts
1 watt = 1 Joule of energy per second
2.50 * 10^8 watts produces 2.50 * 10^8 Joules of heat energy per second.
2.50 * 10^8 J/s * Time = total energy
2.50 * 10^8 * Time = 1.29744 * 10^12
Time = (1.29744 * 10^12) ÷ (2.50 * 10^8)
Time = 5.18976 * 10^3 seconds ÷ 60 sec/min = 86.496 minutes
WOW
In approximately 1 ½ hours, 500,000 kg of water is heated from room temperature, 20°C, to the boiling point of water, 100°C, and completely converted into 100°C steam!!!
500,000 kg = 500,000 liters
At standard temperature and pressure, pure steam (unmixed with air, but in equilibrium with liquid water) occupies about 1,600 times the volume of an equal mass of liquid water.
Volume = 500,000 * 1,600 = 8.0 * 10^8 liters at C°K
At 100°C = 373°K, the volume = 373/273 * 8.0 * 10^8 = 1.093 * 10^9 Liters
Before the accident, the volume of the 20°C water = 500,000 liters
After the accident, the volume of the 100° steam = 1.093 * 10^9 liters
Ratio of volume after to volume before the accident = 1.093 * 10^9 / 500,000 = 2.186 * 10^3
This ratio of the volume after to the volume before the accident = ratio of the pressure after to the pressure before the accident.
The pressure after the accident is 2186 times the pressure before the accident.
This means the pressure inside tank that usually contains 500,000 liters of 100°C water at 1 atmosphere pressure now contains 1.093 * 10^9 liters of 100°C steam at 2186 atmosphere pressure.
Now you know why the building that contains the nuclear reactor is a thick reinforced concrete wall in the shape of hemisphere.
2186 atmosphere of pressure would explode the roof off a normal building and spread radioactive particles all over the land and air and water.
Our nuclear reactors are designed so the graphite moderator components are not exposed when the reactor vessel ruptures allowing the 500,000 liters of coolant water to overheat causing the pressure to increase to a pressure that is 2186 times the pressure before the accident.
3)
Isothermal compressions starting from the same V and T...
W/W = ln(V3/V1) ÷ ln(V2/V1)
V2 = V1/2 then
V3 = V1/20
W = 600 J then...
(for 20th) W = (600 J)*(ln 20)/(ln 2)
= -2 593.2 kJ