Expand your knowledge base with the help of IDNLearn.com's extensive answer archive. Ask your questions and receive detailed and reliable answers from our experienced and knowledgeable community members.
Sagot :
Sure! Let's solve this step-by-step.
### Step 1: Given values
- Mass of water (m): 1299.1 grams
- Heat absorbed (Q): 65.12 kJ
- Initial temperature (T_initial): 7°C
- Specific heat capacity of water (c): [tex]\(4.18 \, \text{J/g°C}\)[/tex]
### Step 2: Convert heat absorbed from kJ to J
We know that [tex]\( 1 \, \text{kJ} = 1000 \, \text{J} \)[/tex]. So we convert the heat absorbed from kJ to J:
[tex]\[ Q = 65.12 \, \text{kJ} \times 1000 \, \frac{\text{J}}{\text{kJ}} = 65120 \, \text{J} \][/tex]
### Step 3: Calculate the change in temperature
We use the formula:
[tex]\[ Q = m \cdot c \cdot \Delta T \][/tex]
Where [tex]\( \Delta T \)[/tex] is the change in temperature.
Solving for [tex]\( \Delta T \)[/tex]:
[tex]\[ \Delta T = \frac{Q}{m \cdot c} \][/tex]
Substitute the given values:
[tex]\[ \Delta T = \frac{65120 \, \text{J}}{1299.1 \, \text{g} \times 4.18 \, \text{J/g°C}} \][/tex]
[tex]\[ \Delta T \approx 11.99°C \][/tex]
### Step 4: Calculate the final temperature
We add the change in temperature to the initial temperature to find the final temperature:
[tex]\[ T_{\text{final}} = T_{\text{initial}} + \Delta T \][/tex]
[tex]\[ T_{\text{final}} = 7°C + 11.99°C \][/tex]
[tex]\[ T_{\text{final}} \approx 18.99°C \][/tex]
### Summary
Thus, after absorbing 65.12 kJ of heat, the final temperature of the water sample will be approximately 18.99°C.
### Step 1: Given values
- Mass of water (m): 1299.1 grams
- Heat absorbed (Q): 65.12 kJ
- Initial temperature (T_initial): 7°C
- Specific heat capacity of water (c): [tex]\(4.18 \, \text{J/g°C}\)[/tex]
### Step 2: Convert heat absorbed from kJ to J
We know that [tex]\( 1 \, \text{kJ} = 1000 \, \text{J} \)[/tex]. So we convert the heat absorbed from kJ to J:
[tex]\[ Q = 65.12 \, \text{kJ} \times 1000 \, \frac{\text{J}}{\text{kJ}} = 65120 \, \text{J} \][/tex]
### Step 3: Calculate the change in temperature
We use the formula:
[tex]\[ Q = m \cdot c \cdot \Delta T \][/tex]
Where [tex]\( \Delta T \)[/tex] is the change in temperature.
Solving for [tex]\( \Delta T \)[/tex]:
[tex]\[ \Delta T = \frac{Q}{m \cdot c} \][/tex]
Substitute the given values:
[tex]\[ \Delta T = \frac{65120 \, \text{J}}{1299.1 \, \text{g} \times 4.18 \, \text{J/g°C}} \][/tex]
[tex]\[ \Delta T \approx 11.99°C \][/tex]
### Step 4: Calculate the final temperature
We add the change in temperature to the initial temperature to find the final temperature:
[tex]\[ T_{\text{final}} = T_{\text{initial}} + \Delta T \][/tex]
[tex]\[ T_{\text{final}} = 7°C + 11.99°C \][/tex]
[tex]\[ T_{\text{final}} \approx 18.99°C \][/tex]
### Summary
Thus, after absorbing 65.12 kJ of heat, the final temperature of the water sample will be approximately 18.99°C.
We appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. Thank you for choosing IDNLearn.com for your queries. We’re committed to providing accurate answers, so visit us again soon.