Silver pellets with a mass of 1.0 g and a temperature of 85°C are added to 200 g of water at 18°C. How many pellets must be added to increase the equilibrium temperature of the system to 24°C?
To solve this problem, we need to use the principle of heat transfer, specifically the equation for heat gained or lost by an object:
Q = m * c * ΔT
where Q is the heat gained or lost, m is the mass of the object, c is the specific heat capacity of the substance, and ΔT is the change in temperature.
Let's break down the problem step by step:
1. Identify the heat gained by the silver pellets:
- The mass of the silver pellets is given as 1.0 g.
- The initial temperature of the silver pellets is 85°C, and they need to reach 24°C.
- The specific heat capacity of silver is 0.235 J/g°C.
Using the equation Q = m * c * ΔT, we can calculate the heat gained by the silver pellets.
Q = (1.0 g) * (0.235 J/g°C) * (24°C - 85°C)
2. Identify the heat lost by the water:
- The mass of the water is given as 200 g.
- The initial temperature of the water is 18°C, and the final temperature needs to be 24°C.
- The specific heat capacity of water is 4.18 J/g°C.
Using the equation Q = m * c * ΔT, we can calculate the heat lost by the water.
Q = (200 g) * (4.18 J/g°C) * (24°C - 18°C)
3. Set up an equation and solve for the number of silver pellets:
- The heat gained by the silver pellets should be equal to the heat lost by the water to reach equilibrium. Therefore, we can set up the equation:
(1.0 g) * (0.235 J/g°C) * (24°C - 85°C) = (200 g) * (4.18 J/g°C) * (24°C - 18°C)
Now, let's calculate the number of silver pellets needed to increase the equilibrium temperature.
Number of pellets = (200 g) * (4.18 J/g°C) * (24°C - 18°C) / ((1.0 g) * (0.235 J/g°C) * (24°C - 85°C))
By plugging in the values and performing the calculation, you will find the number of pellets needed to increase the equilibrium temperature to 24°C.