Question

An ideal gas goes from an initial state to final state. During the process, the pressure of the gas increases linearly with temperature.
A. The work done by gas during the process is zero.
B. The heat added to the gas is different from the change in its internal energy.
C. The volume of the gas is increased.
D. The internal energy of the gas is increased.
E. The process is isochoric (constant volume process).
Choose the correct answer from the options given below:

• A. A, B, C, D Only
• B. A, D, E Only
• C. E Only
• D. A, C Only

Hint:

In processes involving ideal gases, when the volume remains constant, the work done is zero. The heat added in such a case is equal to the change in internal energy. This type of process is called an isochoric process.

Answer 1

The Correct Option is B

Individual analysis of the provided processes is as follows:

• Option A: The work performed by the gas is zero.

In thermodynamics, work done by a gas is zero during an isochoric process, characterized by constant volume. If the question implies that pressure increases linearly with temperature, and option E is accurate, then the gas undergoes an isochoric process. Consequently, the work performed is indeed zero under these circumstances.

• Option B: The heat supplied to the gas differs from the change in its internal energy.

For an ideal gas, the change in internal energy (\(\(\Delta U\)\)) is directly proportional to the change in temperature (\(\(\Delta T\)\)). According to the first law of thermodynamics:

\(\Delta Q = \Delta U + \Delta W\)

Given that option E suggests an isochoric process, \(\Delta W = 0\). Therefore, \(\Delta Q = \Delta U\). This option is incorrect under an isochoric process.

• Option C: The volume of the gas expands.

If pressure increases linearly with temperature and volume remains constant, the volume does not increase. Hence, this option is also incorrect.

• Option D: The internal energy of the gas increases.

The internal energy of an ideal gas is a function of temperature. As temperature rises (indicated by the linear increase in pressure with temperature), the internal energy increases. Thus, option D is correct.

• Option E: The process is isochoric (constant volume).

A linear relationship between pressure and temperature, as per the ideal gas law \(PV = nRT\), implies that the volume remains constant. A linear increase of pressure with temperature typically defines an isochoric process where volume is invariant.

Upon reviewing all options, only A, D, and E are deemed correct. The final answer is therefore:

A, D, E Only