A 100 kg steam boiler is made of steel and contains 200 kg of water at 5.00°C. How much heat is required to raise the temperature of both the boiler and water to 100°C?
The specific heat of Steel is 0.115kcal/kg°C. The specific heat of Water is 1.00kcal/kg°C
1 Cal = 4180 J.
Q = ΔU1 + ΔU2 =
=c1•m1 •ΔT + c2•m2 •ΔT =
= ΔT •(c1•m1 + c2•m2 ) =
= 95• (4180•0.115•100 + 4180•200)= =8.4•10^7 J
To calculate the heat required to raise the temperature of both the boiler and water, we need to consider the specific heat capacities of steel and water.
The heat required to raise the temperature of an object can be calculated using the formula:
Heat = mass × specific heat × change in temperature
In this case, we have two objects: the steel boiler and the water inside it. Let's calculate the heat required for each object separately and then add them together.
1. Heat required for the steel boiler:
Mass of the steel boiler = 100 kg
Specific heat of steel = 0.115 kcal/kg°C
Initial temperature of the steel boiler = 5.00°C
Final temperature of the steel boiler = 100°C
Change in temperature of the steel boiler = Final temperature - Initial temperature
= 100°C - 5.00°C
= 95.00°C
Heat required for the steel boiler = mass × specific heat × change in temperature
= 100 kg × 0.115 kcal/kg°C × 95.00°C
2. Heat required for the water:
Mass of water = 200 kg
Specific heat of water = 1.00 kcal/kg°C
Initial temperature of water = 5.00°C
Final temperature of water = 100°C
Change in temperature of the water = Final temperature - Initial temperature
= 100°C - 5.00°C
= 95.00°C
Heat required for the water = mass × specific heat × change in temperature
= 200 kg × 1.00 kcal/kg°C × 95.00°C
Now, let's add the heat required for both the steel boiler and water:
Total heat required = Heat required for the steel boiler + Heat required for the water
Substituting the values into the equation, we get:
Total heat required = (100 kg × 0.115 kcal/kg°C × 95.00°C) + (200 kg × 1.00 kcal/kg°C × 95.00°C)