
(Molar specific heat capacity at constant pressure) – (Molar specific heat capacity at constant volume) is equal to
(A) R
(B) P
(C) V
(D) T
Answer
442.5k+ views
1 likes
Hint: To understand and solve this question, we will have to first understand the molar specific heat capacity at constant pressure and at constant volume. We will also use the relationship between them to finally get our solution.
Complete answer:
First let us understand what molar specific heat capacity is at constant pressure and at constant volume.
Molar specific heat capacity at constant pressure is defined as the amount of heat energy required to raise the temperature of one mole of a substance through or at constant pressure. It is denoted by .
By definition,
Since,
Therefore,
Molar specific heat capacity at constant volume is defined as the amount of heat energy required to raise the temperature of one mole of a substance through or at constant volume. It is denoted by .
By definition,
Since,
Therefore,
Now let’s see the relationship between molar specific heat capacity at constant pressure and at constant volume.
From the equation of enthalpy,
But, in case of one mole of ideal gas,
Therefore,
On differentiating the both sides with respect to temperature, we get,
But we know that, and
Therefore,
Or we can say,
Thus, the difference between the molar heat capacities at constant volume and pressure always equals , the universal gas constant.
Hence, option A is correct.
Note:
In exams, you need not to memorize the whole thing. You can just remember the relationship between molar specific heat capacity at constant volume and at constant pressure for one mole, that is, . You can also derive the relation between the two by simply using the enthalpy equation.
Complete answer:
First let us understand what molar specific heat capacity is at constant pressure and at constant volume.
Molar specific heat capacity at constant pressure is defined as the amount of heat energy required to raise the temperature of one mole of a substance through
By definition,
Since,
Therefore,
Molar specific heat capacity at constant volume is defined as the amount of heat energy required to raise the temperature of one mole of a substance through
By definition,
Since,
Therefore,
Now let’s see the relationship between molar specific heat capacity at constant pressure and at constant volume.
From the equation of enthalpy,
But, in case of one mole of ideal gas,
Therefore,
On differentiating the both sides with respect to temperature, we get,
But we know that,
Therefore,
Or we can say,
Thus, the difference between the molar heat capacities at constant volume and pressure always equals
Hence, option A is correct.
Note:
In exams, you need not to memorize the whole thing. You can just remember the relationship between molar specific heat capacity at constant volume and at constant pressure for one mole, that is,
Latest Vedantu courses for you
Grade 10 | CBSE | SCHOOL | English
Vedantu 10 CBSE Pro Course - (2025-26)
School Full course for CBSE students
₹37,300 per year
Recently Updated Pages
Master Class 11 Business Studies: Engaging Questions & Answers for Success

Master Class 11 Economics: Engaging Questions & Answers for Success

Master Class 11 Accountancy: Engaging Questions & Answers for Success

Master Class 11 Computer Science: Engaging Questions & Answers for Success

Master Class 11 English: Engaging Questions & Answers for Success

Master Class 11 Maths: Engaging Questions & Answers for Success

Trending doubts
Which one is a true fish A Jellyfish B Starfish C Dogfish class 11 biology CBSE

Difference Between Prokaryotic Cells and Eukaryotic Cells

1 ton equals to A 100 kg B 1000 kg C 10 kg D 10000 class 11 physics CBSE

One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE

How much is 23 kg in pounds class 11 chemistry CBSE

Net gain of ATP in glycolysis a 6 b 2 c 4 d 8 class 11 biology CBSE
