
The temperature of 3 kg of nitrogen is raised from to . Compute the difference in work done if heating were at constant pressure and at constant volume.
( For nitrogen & )
A. 81000 J
B. 64000 J
C. 49000 J
D. 36000 J
Answer
490.2k+ views
Hint:-First find the number of moles in 3kg of nitrogen , then use the formula work done to raise the temperature of n number of moles by at constant pressure ( ) and also for work done to raise the temperature of n number of moles by at constant volume ( ).
After finding all the differences by subtracting , this is the required answer.
Complete step-by-step solution:
Work done to raise the temperature from to at constant pressure
Work done to raise the temperature from to at constant volume
Since in both the cases the temperature is increasing by the same degree so change in internal energy for both the cases is the same.
Difference in work done if heating were at constant pressure and at constant volume is given by
By simplifying the relation we get,
We know that
Finding the numbers of moles of nitrogen in 3kg.
&
Putting all the values we get,
By solving this we get with
Since , the difference in work done if heating were at constant pressure and at constant volume is .
Hence option (A) is the correct answer.
Note:- Work done to increase the temperature of gases at constant pressure is always greater than the work done to increase the temperature by the same amount of gases at constant volume.
However, in both the cases the temperature is increasing by the same degree so change in internal energy for both the cases is the same.
After finding all the differences by subtracting , this is the required answer.
Complete step-by-step solution:
Work done to raise the temperature from
Work done to raise the temperature from
Since in both the cases the temperature is increasing by the same degree so change in internal energy for both the cases is the same.
Difference in work done if heating were at constant pressure and at constant volume is given by
By simplifying the relation we get,
We know that
Finding the numbers of moles of nitrogen in 3kg.
Putting all the values we get,
By solving this we get with
Since , the difference in work done if heating were at constant pressure and at constant volume is
Hence option (A) is the correct answer.
Note:- Work done to increase the temperature of gases at constant pressure is always greater than the work done to increase the temperature by the same amount of gases at constant volume.
However, in both the cases the temperature is increasing by the same degree so change in internal energy for both the cases is the same.
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