A small block of ice at 0∘C is subjected to 12 g of 100∘C steam and melts completely. Find the maximum mass of the block of ice?
To find the maximum mass of the block of ice, we need to consider the concept of heat transfer.
When the steam is added to the ice, it will transfer heat to the ice until both reach the same final temperature. This is known as the principle of thermal equilibrium.
The heat transferred between two substances can be calculated using the formula:
Q = m * c * ΔT
Where:
- Q is the heat transferred
- m is the mass of the substance
- c is the specific heat capacity of the substance
- ΔT is the change in temperature
In this case, we know the initial and final temperatures of both the ice and steam, so we can calculate the heat transferred.
Let's calculate the heat transferred from the steam to the ice:
Q_ice = m_ice * c_ice * ΔT_ice
And the heat transferred from the ice to the steam:
Q_steam = m_steam * c_steam * ΔT_steam
Since the ice melts completely, the final temperature of both the ice and steam will be 0°C. Therefore, ΔT_ice = 0 and ΔT_steam = 100°C.
The specific heat capacity of ice is approximately 2.09 J/g°C, and the specific heat capacity of steam is approximately 2.03 J/g°C.
Now, let's plug in the values and calculate the heat transferred:
Q_ice = m_ice * 2.09 * 0 = 0 (Since ΔT_ice = 0)
Q_steam = 12 g * 2.03 J/g°C * 100°C = 2436 J
Since the heat transferred from the steam to the ice is equal to the heat transferred from the ice to the steam (due to thermal equilibrium), we have:
Q_steam = Q_ice
2436 J = 0
This equation tells us that the heat transferred from the steam is greater than the heat required to melt the ice. As a result, all the steam will not be condensed, and the maximum mass of the block of ice is zero.