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QPage 60: Q10: HC Verma: Concepts of Physics - Volume 2 Laws of Thermodynamics Page 60: Q10 Solution: An ideal gas is pumped into a rigid container having diathermic …

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often assume internal energy depends only on temperature for an ideal gas, ignoring that the system is open and the number of moles ($n$) changes. You must recognize that $U = nC_vT$ scales with mass, so doubling $n$ at constant $T$ doubles $U$.

An ideal gas is pumped into a rigid container having diathermic walls so that the temperature remains constant. In a certain time interval, the pressure in the container is doubled. Is the internal energy of the contents of the container also doubled in the interval?

Step-by-Step Verified Solution

**Answer:** Yes, the internal energy of the contents is also doubled. **Step-by-Step Explanation:** For an ideal gas,

U = nC_vT

. The container is rigid (constant volume) and diathermic (constant temperature). Since pressure doubles at constant

T

and

V

, the number of moles must double:

n_2 = 2n_1

. Thus,

U_2 = n_2C_vT = 2n_1C_vT = 2U_1

. Internal energy doubles [citation:8][citation:10].

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