How much heat is required to change a 35.8 g ice cube from ice at -12.7°C to water at 45°C? (if necessary, use cice=2090 J/kg°C and csteam= 2010 J/kg°C)How much heat is required to change a 35.8 g ice cube from ice at -12.7°C to steam at 113°C?
To calculate the heat required to change an ice cube from ice at a certain temperature to water at a certain temperature, we need to consider the following steps:
1. Calculate the heat required to warm up the ice cube from -12.7°C to its melting point at 0°C.
2. Calculate the heat required to melt the ice cube at 0°C.
3. Calculate the heat required to warm up the resulting water from 0°C to the desired final temperature (45°C).
Step 1: Calculate the heat required to warm up the ice cube from -12.7°C to 0°C.
To calculate this heat, we use the specific heat capacity of ice (cice), which is given as 2090 J/kg°C.
Q1 = mass × cice × ΔT
= 35.8 g × (1 kg / 1000 g) × 2090 J/kg°C × (0°C - (-12.7°C))
Step 2: Calculate the heat required to melt the ice cube at 0°C.
To calculate this heat, we use the heat of fusion (or latent heat) of ice, which is 334 kJ/kg.
Q2 = mass × heat of fusion
= 35.8 g × (1 kg / 1000 g) × 334,000 J/kg
Step 3: Calculate the heat required to warm up the resulting water from 0°C to 45°C.
To calculate this heat, we use the specific heat capacity of water, which is usually considered to be 4180 J/kg°C.
Q3 = mass × cwater × ΔT
= 35.8 g × (1 kg / 1000 g) × 4180 J/kg°C × (45°C - 0°C)
To find the total heat required to change the ice cube to water at 45°C, we sum up Q1, Q2, and Q3.
Total heat = Q1 + Q2 + Q3
Using the given values and performing the calculations, you should be able to find the answer.
Similarly, you can follow the same steps to calculate the heat required to change the ice cube from -12.7°C to steam at 113°C. However, in this case, you would need to consider the additional steps of:
4. Calculate the heat required to vaporize the water at 100°C.
5. Calculate the heat required to warm up the resulting steam from 100°C to 113°C.
For step 4, you would use the heat of vaporization (or latent heat) of water, which is typically around 2,260 kJ/kg.
For step 5, you would use the specific heat capacity of steam (csteam), which is given as 2010 J/kg°C.
Following the same calculation steps as before, you can find the total heat required to change the ice cube to steam at 113°C.