A copper container of mass 100g contains 500g of water. A steel paddle of mass 85g stirs the water. A pulley system operates the paddle.
A) the mass (15kg) drops 2,4m, turning the steel paddle. Assume heat lost to surrounding is negligible.
1. Find the energy transfered to the container,water and paddle.
2. Find the rise in temperature of the water.
3. Assume that the rise in temperature of the steel paddle is the same as that of the water when the energy is transferred from the pulley system to the water. Find the energy needed to raise temperature of 1kg steel paddle by 1 degree Celsius.
a. gravitational energy=heatinwater, assuming the dropping mass did not gain velocity.
b. masscopper*cc*deltaT+masspaddle*c*deltaT+masswater*cw*deltaTemp=total energy in
To solve this problem, we need to apply the principles of work and energy, as well as specific heat capacity.
1. Let's start by finding the energy transferred to the container, water, and paddle.
- The mass of the container is given as 100g, which is 0.1kg.
- The mass of water is given as 500g, which is 0.5kg.
- The mass of the paddle is given as 85g, which is 0.085kg.
- The height through which the mass drops is given as 2.4m.
- The acceleration due to gravity is approximately 9.8 m/s^2.
The potential energy lost by the mass is given by the formula: Potential Energy = mass * gravitational acceleration * height. Thus, Potential Energy = (15kg) * (9.8 m/s^2) * (2.4m).
To calculate the total energy transfer, we need to consider the energy transferred to the container, water, and paddle.
Energy transferred to the container: Since the container is made of copper, a good conductor of heat, it quickly absorbs and distributes the energy throughout. So, we can assume that the energy transferred to the container is equal to the potential energy lost by the mass.
Energy transferred to the water: The energy transferred to the water can be calculated using the formula: Energy = mass * specific heat capacity * change in temperature. The specific heat capacity of water is approximately 4186 J/kg°C.
Energy transferred to the paddle: Since it is stated that the rise in temperature of the paddle is the same as that of the water when the energy is transferred, we can calculate the energy transferred to the paddle using the same formula as for the water.
2. To find the rise in temperature of the water, we need to determine the change in temperature using the energy transferred to the water calculated in the previous step. The formula to calculate the change in temperature is: Change in temperature = Energy transferred / (mass * specific heat capacity).
3. To find the energy needed to raise the temperature of 1kg steel paddle by 1 degree Celsius, we can simply use the energy transferred to the paddle calculated in the first step. Divide that value by the mass of the paddle, which is 0.085kg.
I hope this explanation helps you understand how to approach and solve this problem.