How much heat do I need to convert 200g of liquid water at -25C to water at 30C?. The specific heat capacity of H2O(s) is 2.1 J g*C
To calculate the amount of heat needed to convert 200g of liquid water at -25C to water at 30C, we need to consider two steps:
1. The amount of heat needed to raise the temperature of 200g of water from -25C to 0C.
2. The amount of heat needed to raise the temperature of 200g of ice (at 0C) to 30C.
Let's calculate each step:
Step 1: Raising the temperature of 200g of water from -25C to 0C.
The specific heat capacity of H2O(s) at this temperature is 2.1 J/g*C.
The formula to calculate the heat energy (Q) is:
Q = mass (m) x specific heat capacity (c) x change in temperature (ΔT)
Q1 = 200g x 2.1 J/g*C x (0C - (-25C))
Q1 = 200g x 2.1 J/g*C x 25C
Q1 = 200g x 52.5 J
Q1 = 10,500 J
So, the amount of heat needed to raise the temperature of 200g of water from -25C to 0C is 10,500 J.
Step 2: Raising the temperature of 200g of ice from 0C to 30C.
Since ice is at its melting point, we need to consider the heat energy required for both phase change (melting) and temperature change.
The heat energy required for phase change (melting) can be calculated using the formula:
Q2 = mass (m) x heat of fusion (ΔHf)
The heat of fusion (ΔHf) for water is 334 J/g.
Q2 = 200g x 334 J/g
Q2 = 66,800 J
The heat energy required for temperature change can be calculated using the same formula as step 1:
Q3 = mass (m) x specific heat capacity (c) x change in temperature (ΔT)
Q3 = 200g x 4.18 J/g*C x (30C - 0C)
Q3 = 200g x 4.18 J/g*C x 30C
Q3 = 25,080 J
So, the total amount of heat needed to raise the temperature of 200g of liquid water at -25C to water at 30C is:
Total heat = Q1 + Q2 + Q3
Total heat = 10,500 J + 66,800 J + 25,080 J
Total heat = 102,380 J
Therefore, you would need 102,380 J of heat to convert 200g of liquid water at -25C to water at 30C.