one liter of water at atmospheric pressure ismixed with 9 liter of water of 25 degrees at an atmospheric pressure in an insulated tank .find the temprature of tank.options are 1)25 2)32.5 3)30 4) 24........pls. help
To find the temperature of the tank after mixing the water, we can use the principle of conservation of energy.
We know that the heat gained by the cold water (initially at 25°C) is equal to the heat lost by the hot water (initially at an unknown temperature, let's call it T).
The heat gained by the cold water can be calculated using the specific heat capacity of water (which is approximately 4.18 J/g·°C) and the mass of water (9 liters = 9000 grams):
Heat gained = (mass of cold water) × (specific heat capacity of water) × (change in temperature)
= 9000 g × 4.18 J/g·°C × (T - 25°C)
The heat lost by the hot water can be calculated using the specific heat capacity of water and the mass of water (1 liter = 1000 grams):
Heat lost = (mass of hot water) × (specific heat capacity of water) × (change in temperature)
= 1000 g × 4.18 J/g·°C × (T - initial temperature of hot water)
Since the tank is insulated, the total heat gained by the cold water must be equal to the total heat lost by the hot water:
9000 g × 4.18 J/g·°C × (T - 25°C) = 1000 g × 4.18 J/g·°C × (T - initial temperature of hot water)
Simplifying the equation:
9(T - 25) = (T - initial temperature)
Expanding the equation:
9T - 225 = T - initial temperature
Combining like terms:
8T = 225 - initial temperature
Finally, rearranging the equation to isolate T, the temperature of the tank:
T = (225 - initial temperature) / 8
Since we don't have the initial temperature, we can't determine the exact temperature of the tank. Therefore, none of the provided options (25, 32.5, 30, and 24) can be chosen with certainty without additional information.