1. 500 g of aluminium block at a temperature of 650 degrees Celsius is dropped into a copper calorimeter of mass 100g containing 800 g of water at 30 degree celsius. calculate the maximum temperature of the mixture .(specific heat capacity of water ,copper and aluminium are 4200 400 and 900 respectively.)
2. An electric kettle of mass 0.5 kg rated 1W contains liquid of mass 1.5 kg .calculate the specific heat capacity of the liquid if it is heated from 30 degrees Celsius to 80 degrees Celsius in 5 minutes .(specific heat capacity of the material of the kettle is 900.)
3. Calculate the time it takes 1,000W heater to increase the temperature of 30 kg of copper block from 25 degrees Celsius to 125 degrees Celsius if the specific heat capacity of copper is 400.
4. A brass sphere of 500 kg and specific heat capacity 3800 is produced dropped from a height of 500 m .what is the rise in temperature of the sphere if all the potential energy at the top is transformed to heat energy.
5. Waterfalls through a height of 50 cm. Determine the temperature rise of the water at the bottom of the fall.(neglect energy losses .specific heat capacity of water is 4200.)
6. How long will it take to heat 3 kg of water from 28 degrees Celsius to 88 degrees Celsius in an electric kettle taking 6A from a 220V supply specific heat capacity of water is 4180.
7. An electric drill rated 400W is used to drill a hole in a copper of mass 400 g in 20 seconds. calculate the rise in temperature if all the heat produced is absorbed by the copper .(specific heat capacity of copper is 400.)
1. First, calculate the heat lost by the aluminium block:
Q = mcΔT
Q = 500g * 900 J/kg°C * (650°C - T)
Q = 450000J - 900T
Then, calculate the heat gained by the water and copper calorimeter:
Q = mcΔT + mcΔT
Q = (100g * 400 J/kg°C + 800g * 4200 J/kg°C) * (T - 30°C)
Q = 420000T - 12600000
Set the two equations equal to each other:
450000 - 900T = 420000T - 12600000
186000T = 1305000
T = 7°C
2. First, calculate the heat energy required to raise the temperature of the liquid:
Q = mcΔT
Q = (0.5kg + 1.5kg) * c * (80°C - 30°C)
Q = 2kg * c * 50°C
Q = 100c
Power = Energy / Time
1W = 100c / (5 * 60)
c = 1/300 J/g°C
3. First, calculate the heat energy required to raise the temperature of the copper block:
Q = mcΔT
Q = 30kg * 400 J/kg°C * (125°C - 25°C)
Q = 30kg * 400 J/kg°C * 100°C
Q = 1200000J
Power = Energy / Time
1000W = 1200000J / t
t = 1200 seconds = 20 minutes
4. Potential energy = mgh
Potential energy = 500kg * 9.81m/s^2 * 500m
Potential energy = 2452500 J
All potential energy is converted to heat energy:
Q = mcΔT
2452500 J = 500kg * 3800 J/kg°C * ΔT
ΔT = 1.288°C
5. Potential energy = mgh
Potential energy = 1kg * 9.81m/s^2 * 0.5m
Potential energy = 4.905 J
All potential energy is converted to heat energy:
Q = mcΔT
4.905 J = 1kg * 4200 J/kg°C * ΔT
ΔT = 0.001°C
6. First, calculate the heat energy required to raise the temperature of the water:
Q = mcΔT
Q = 3kg * 4180 J/kg°C * (88°C - 28°C)
Q = 3kg * 4180 J/kg°C * 60°C
Q = 752400J
Power = Energy / Time
6A * 220V = 752400J / t
t = 18.8 seconds
7. Power = mcΔT/t
400W = 400g * 400 J/kg°C * ΔT / 20s
ΔT = 0.05°C