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Answer :
To find out how much energy is required to raise the temperature of 13.5 grams of gaseous hydrogen from 22.1 °C to 36.9 °C, we need to use the formula for calculating heat energy:
[tex]\[ Q = m \times c \times \Delta T \][/tex]
where:
- [tex]\( Q \)[/tex] is the heat energy in joules,
- [tex]\( m \)[/tex] is the mass in grams,
- [tex]\( c \)[/tex] is the specific heat capacity in J/g°C,
- [tex]\( \Delta T \)[/tex] is the change in temperature in °C.
Let's break it down step-by-step:
1. Identify the Given Values:
- Mass of hydrogen ([tex]\( m \)[/tex]): 13.5 grams
- Specific heat capacity of gaseous hydrogen ([tex]\( c \)[/tex]): 14.304 J/g°C
- Initial temperature: 22.1 °C
- Final temperature: 36.9 °C
2. Calculate the Temperature Change ([tex]\( \Delta T \)[/tex]):
[tex]\[
\Delta T = \text{Final temperature} - \text{Initial temperature} = 36.9 \, ^\circ \text{C} - 22.1 \, ^\circ \text{C} = 14.8 \, ^\circ \text{C}
\][/tex]
3. Calculate the Energy Required ([tex]\( Q \)[/tex]):
Plug the values into the formula:
[tex]\[
Q = 13.5 \, \text{g} \times 14.304 \, \text{J/g°C} \times 14.8 \, ^\circ \text{C}
\][/tex]
[tex]\[
Q \approx 2857.94 \, \text{J}
\][/tex]
Thus, the amount of energy required to raise the temperature of 13.5 grams of gaseous hydrogen from 22.1 °C to 36.9 °C is approximately 2857.94 joules.
[tex]\[ Q = m \times c \times \Delta T \][/tex]
where:
- [tex]\( Q \)[/tex] is the heat energy in joules,
- [tex]\( m \)[/tex] is the mass in grams,
- [tex]\( c \)[/tex] is the specific heat capacity in J/g°C,
- [tex]\( \Delta T \)[/tex] is the change in temperature in °C.
Let's break it down step-by-step:
1. Identify the Given Values:
- Mass of hydrogen ([tex]\( m \)[/tex]): 13.5 grams
- Specific heat capacity of gaseous hydrogen ([tex]\( c \)[/tex]): 14.304 J/g°C
- Initial temperature: 22.1 °C
- Final temperature: 36.9 °C
2. Calculate the Temperature Change ([tex]\( \Delta T \)[/tex]):
[tex]\[
\Delta T = \text{Final temperature} - \text{Initial temperature} = 36.9 \, ^\circ \text{C} - 22.1 \, ^\circ \text{C} = 14.8 \, ^\circ \text{C}
\][/tex]
3. Calculate the Energy Required ([tex]\( Q \)[/tex]):
Plug the values into the formula:
[tex]\[
Q = 13.5 \, \text{g} \times 14.304 \, \text{J/g°C} \times 14.8 \, ^\circ \text{C}
\][/tex]
[tex]\[
Q \approx 2857.94 \, \text{J}
\][/tex]
Thus, the amount of energy required to raise the temperature of 13.5 grams of gaseous hydrogen from 22.1 °C to 36.9 °C is approximately 2857.94 joules.
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