A heat transfer of 9.5 x 10^5 J is required to convert a block of ice at -15°C to water at 15°C. What is the mass of the block of ice?
Need help
To find the mass of the block of ice, we can use the specific heat capacity and the heat transfer formula:
Q = mcΔT
Where:
Q is the heat transfer
m is the mass of the object
c is the specific heat capacity
ΔT is the change in temperature
Given:
Q = 9.5 x 10^5 J
c for ice = 2.09 x 10^3 J/(kg·°C)
ΔT = 15°C - (-15°C) = 30°C
Plugging in the values, we get:
9.5 x 10^5 J = m × (2.09 x 10^3 J/(kg·°C)) × 30°C
Now, we solve for m (the mass of the block of ice):
m = (9.5 x 10^5 J) / [(2.09 x 10^3 J/(kg·°C)) × 30°C]
m = (9.5 x 10^5 J) / (62.7 x 10^3 J/(kg·°C))
m = 15.165 kg
Therefore, the mass of the block of ice is approximately 15.165 kg.
To find the mass of the block of ice, we need to use the specific heat capacity equation:
Q = mcΔT
Where:
Q is the heat transfer (9.5 x 10^5 J)
m is the mass of the block of ice (unknown)
c is the specific heat capacity (for ice, it is approximately 2.09 J/g°C)
ΔT is the change in temperature (15°C - (-15°C) = 30°C)
We can rearrange the equation to solve for the mass (m):
m = Q / (c * ΔT)
Substituting the values we know:
m = (9.5 x 10^5 J) / (2.09 J/g°C * 30°C)
Now we can calculate the mass of the block of ice:
m = (9.5 x 10^5 J) / (2.09 J/g°C * 30°C)
m ≈ 1637.28 g (rounded to two decimal places)
Therefore, the mass of the block of ice is approximately 1637.28 grams.