5. An aluminium cessel of mass 200g, contains 0.5 litre of water. What is the heat required to raise the temperature of the system from 25 Degree centigrade to 75 Degree centigrade? (S.H.C of Aluminium 0.84X10^3J/kg dehree centigrade and S.H.C of water 4.2X10^3J/kg dehree centigrade. A dencity water = 10^3/m^3)
To calculate the heat required to raise the temperature of the system, we need to find the total heat required to heat both the aluminum vessel and the water.
First, let's find the heat required for the aluminum vessel:
- We have the specific heat capacity (S.H.C) of aluminum, which is given as 0.84 x 10^3 J/kg°C.
- The mass of the aluminum vessel is given as 200g, but we need to convert it to kilograms by dividing by 1000: 200g ÷ 1000 = 0.2 kg.
- The temperature change for the aluminum vessel is from 25°C to 75°C, so the change in temperature is: (75 - 25) = 50°C.
Now, we can calculate the heat required for the aluminum vessel using the formula:
Heat = mass x specific heat capacity x temperature change.
Heat (vessel) = 0.2 kg x 0.84 x 10^3 J/kg°C x 50°C.
Next, let's find the heat required for the water:
- We have the specific heat capacity (S.H.C) of water, which is given as 4.2 x 10^3 J/kg°C.
- The volume of water is given as 0.5 liters.
To calculate the mass of water, we'll use the formula:
mass = density x volume.
The density of water is given as 10^3 kg/m³, and since 1 liter = 0.001 m³, we can calculate the mass of water:
mass (water) = density x volume = 10^3 kg/m³ x 0.5 x 0.001 m³.
Now, let's calculate the heat required for the water using the formula:
Heat = mass x specific heat capacity x temperature change.
Heat (water) = mass (water) x 4.2 x 10^3 J/kg°C x 50°C.
Finally, to find the total heat required to raise the temperature of the system, we add the heat required for the aluminum vessel and the heat required for the water together:
Total Heat Required = Heat (vessel) + Heat (water).
Now, you can substitute the values into the formulas and calculate the answer.