Answer :
To determine the amount of heat required to raise the temperature of 20 grams of water from 10°C to 30°C, we can use the formula:
[tex]\[ Q = mc\Delta T \][/tex]
where:
- \( Q \) is the heat required,
- \( m \) is the mass of the water,
- \( c \) is the specific heat capacity of water,
- \( \Delta T \) is the change in temperature.
1. Identify the given values:
- Mass of water, \( m = 20 \) grams,
- Specific heat capacity of water, \( c = 4.18 \) J/g°C,
- Initial temperature, \( T_{\text{initial}} = 10 \)°C,
- Final temperature, \( T_{\text{final}} = 30 \)°C.
2. Calculate the change in temperature:
[tex]\[ \Delta T = T_{\text{final}} - T_{\text{initial}} \][/tex]
[tex]\[ \Delta T = 30 \,°C - 10 \,°C \][/tex]
[tex]\[ \Delta T = 20\,°C \][/tex]
3. Substitute the values into the formula:
[tex]\[ Q = mc\Delta T \][/tex]
[tex]\[ Q = (20 \,\text{g}) \times (4.18 \,\text{J/g°C}) \times (20 \,\text{°C}) \][/tex]
4. Calculate:
[tex]\[ Q = 20 \times 4.18 \times 20 \][/tex]
[tex]\[ Q = 1672 \,\text{J} \][/tex]
So, the amount of heat required is 1672 joules.
5. Select the closest option:
Given the options:
- A. 1200 joules
- B. 1500 joules
- C. 1700 joules
- D. 1900 joules
- E. 2000 joules
The closest option to 1672 joules is C. 1700 joules.
Thus, the correct answer is:
[tex]\[ \text{C. 1700 joules} \][/tex]
[tex]\[ Q = mc\Delta T \][/tex]
where:
- \( Q \) is the heat required,
- \( m \) is the mass of the water,
- \( c \) is the specific heat capacity of water,
- \( \Delta T \) is the change in temperature.
1. Identify the given values:
- Mass of water, \( m = 20 \) grams,
- Specific heat capacity of water, \( c = 4.18 \) J/g°C,
- Initial temperature, \( T_{\text{initial}} = 10 \)°C,
- Final temperature, \( T_{\text{final}} = 30 \)°C.
2. Calculate the change in temperature:
[tex]\[ \Delta T = T_{\text{final}} - T_{\text{initial}} \][/tex]
[tex]\[ \Delta T = 30 \,°C - 10 \,°C \][/tex]
[tex]\[ \Delta T = 20\,°C \][/tex]
3. Substitute the values into the formula:
[tex]\[ Q = mc\Delta T \][/tex]
[tex]\[ Q = (20 \,\text{g}) \times (4.18 \,\text{J/g°C}) \times (20 \,\text{°C}) \][/tex]
4. Calculate:
[tex]\[ Q = 20 \times 4.18 \times 20 \][/tex]
[tex]\[ Q = 1672 \,\text{J} \][/tex]
So, the amount of heat required is 1672 joules.
5. Select the closest option:
Given the options:
- A. 1200 joules
- B. 1500 joules
- C. 1700 joules
- D. 1900 joules
- E. 2000 joules
The closest option to 1672 joules is C. 1700 joules.
Thus, the correct answer is:
[tex]\[ \text{C. 1700 joules} \][/tex]
