silver ball= 50g
water= 350 g
water= 0 celcius
equilibrium temperature= 10 celcius
specefic heat capacity of platinum= 230
what is the temperature of furnace?
To determine the temperature of the furnace in this scenario, we can use the principle of heat transfer and the concept of specific heat capacity.
First, we need to calculate the heat exchanged between the silver ball and the water during their temperature equilibration. The formula for calculating heat transfer is:
Q = mcΔT
Where:
Q represents the heat transfer (in joules)
m is the mass of the substances involved (in grams)
c is the specific heat capacity of the substance (in J/g°C)
ΔT is the change in temperature (in °C)
Let's calculate the heat transferred between the silver ball and the water:
For the silver ball:
Mass (m) = 50g
Specific Heat Capacity (c) = Unknown (Let's represent it as "x")
Change in Temperature (ΔT) = (10°C - 0°C) = 10°C
Q1 = 50g * x * 10°C
For the water:
Mass (m) = 350g
Specific Heat Capacity (c) = 4.18 J/g°C (specific heat capacity of water)
Change in Temperature (ΔT) = (10°C - 0°C) = 10°C
Q2 = 350g * 4.18 J/g°C * 10°C
Since the heat lost by the silver ball is equal to the heat gained by the water (assuming no heat loss to the surroundings), we can write the equation:
Q1 = Q2
50g * x * 10°C = 350g * 4.18 J/g°C * 10°C
Now, solve the equation for x (specific heat capacity of the silver ball):
50g * x * 10°C = 350g * 4.18 J/g°C * 10°C
50g * x = 350g * 4.18 J/g°C
x = (350g * 4.18 J/g°C) / 50g
x ≈ 29.4 J/g°C
Therefore, the specific heat capacity of the silver ball is approximately 29.4 J/g°C.
Now that we know the specific heat capacity of the silver ball, we can calculate the heat transfer from the furnace to the silver ball using the same formula as before:
Heat Transfer (Q) = mass (m) * specific heat capacity (c) * change in temperature (ΔT).
Let's assume the change in temperature is from 0°C (initial temperature) to the temperature of the furnace (final temperature). Represent the final temperature of the furnace as "T".
Q = 50g * 29.4 J/g°C * (T - 0°C)
Since the heat transfer is balanced when the ball reaches equilibrium, we can equate this formula to zero:
50g * 29.4 J/g°C * (T - 0°C) = 0
Simplifying the equation:
50g * 29.4 J/g°C * T = 0
50g * 29.4 J/g°C = 0
Dividing both sides by (50g * 29.4 J/g°C):
T = 0
Therefore, the temperature of the furnace is 0°C.