Answer : The heat capacity in joules per degree Celsius and calories per degree Celsius is, [tex]47.6J/^oC[/tex] and [tex]11.4cal/^oC[/tex] respectively.
Explanation : Given,
Mass of nitrogen gas = 45.8 g
Heat capacity of nitrogen gas = [tex]1.04J/g^oC[/tex]
First we have to calculate the heat capacity in joules per degree Celsius.
As, 1 gram of nitrogen gas has heat capacity = [tex]1.04J/^oC[/tex]
So, 45.8 gram of nitrogen gas has heat capacity = [tex]45.8\times 1.04J/^oC=47.6J/^oC[/tex]
Thus, the heat capacity in joules per degree Celsius is [tex]47.6J/^oC[/tex]
Now we have to calculate the heat capacity in calories per degree Celsius.
As we are given the conversion:
[tex]1cal=4.184J\\\\1J=\frac{1}{4.184}cal[/tex]
So, the heat capacity of nitrogen gas = [tex]\frac{1}{4.184}cal\times 47.6\text{ per }^oC=11.4cal/^oC[/tex]
Thus, the heat capacity in calories per degree Celsius is [tex]11.4cal/^oC[/tex]
The heat capacity, in Joules per degree Celsius and in calories per degree Celsius are 47.632 J/g°C and 11.384 cal/g°C respectively.
Given the following data:
To find the heat capacity, in Joules per degree Celsius and in calories per degree Celsius:
By direct proportion:
1 gram of nitrogen gas = 1.04 J/g°C
45.8 grams of nitrogen gas = X J/g°C
Cross-multiplying, we have:
[tex]X = 45.8 \times 1.04[/tex]
X = 47.632 J/g°C.
Therefore, the heat capacity, in Joules per degree Celsius, for 45.8 grams of nitrogen gas is 47.632 J/g°C.
In calories per degree Celsius:
1 calorie = 4.184 Joules
Y calorie = 47.632 Joules
Cross-multiplying, we have:
[tex]Y \times 4.184 = 47.632\\\\Y = \frac{47.632}{4.184}[/tex]
Y = 11.384 cal/g°C.
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