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)
Q = mc*change T
Do it for both the aluminum and the water where m = density * volume.
You'll need to convert mass to kg and liters to m^3.
To calculate the heat required to raise the temperature of the system, we need to consider the specific heat capacities of both the aluminum vessel and the water.
Let's break down the problem and calculate the heat required for each component separately.
First, let's calculate the heat required to raise the temperature of the water.
Given:
- Mass of water (m) = 0.5 liter = 0.5 kg (since the density of water is 10^3 kg/m^3)
- Initial temperature (T1) = 25°C
- Final temperature (T2) = 75°C
- Specific heat capacity of water (Cw) = 4.2 × 10^3 J/kg°C
The heat required to raise the temperature of the water can be calculated using the formula:
Qw = m * Cw * ΔT
Where:
- Qw is the heat required for water
- m is the mass of the water
- Cw is the specific heat capacity of water
- ΔT is the change in temperature = T2 - T1
Plugging in the values:
Qw = (0.5 kg) * (4.2 × 10^3 J/kg°C) * (75°C - 25°C)
= 0.5 * 4.2 × 10^3 * 50
= 1.05 × 10^5 J
The heat required to raise the temperature of the water is 1.05 × 10^5 Joules.
Next, let's calculate the heat required to raise the temperature of the aluminum vessel.
Given:
- Mass of the aluminum vessel (m_aluminum) = 200 g = 0.2 kg
- Specific heat capacity of aluminum (Caluminum) = 0.84 × 10^3 J/kg°C
The heat required to raise the temperature of the aluminum vessel can be calculated using the same formula:
Qaluminum = m_aluminum * Caluminum * ΔT
Where:
- Qaluminum is the heat required for aluminum
- m_aluminum is the mass of the aluminum vessel
- Caluminum is the specific heat capacity of aluminum
- ΔT is the change in temperature = T2 - T1
Plugging in the values:
Qaluminum = (0.2 kg) * (0.84 × 10^3 J/kg°C) * (75°C - 25°C)
= 0.2 * 0.84 × 10^3 * 50
= 8400 J
The heat required to raise the temperature of the aluminum vessel is 8400 Joules.
Now, to find the total heat required to raise the temperature of the system, simply add the heat required for the water and the heat required for the aluminum vessel:
Total heat required = Qw + Qaluminum
= 1.05 × 10^5 J + 8400 J
= 1.13 × 10^5 J
Therefore, the heat required to raise the temperature of the system from 25°C to 75°C is 1.13 × 10^5 Joules.